Andy Burnham is crashing the SNP's conference, but without going anywhere near John Swinney's party gathering in Aberdeen.

By deciding to be in Scotland at the same time he is bound to divert some attention from the first minister to himself as prime minister.

Having said that, Burnham has inadvertently done Swinney a few political favours ahead of the SNP's annual get-together.

Firstly, there was an exchange in the Commons where the PM appeared to acknowledge circumstances in which another independence referendum would be legitimate.

He has since pulled back from those comments and returned to the position that the subject is "off limits" - but his earlier remarks are still recorded on the parliamentary record.

Secondly, there was Burnham's Labour conference speech where he said that John Swinney's claim that he could be the last prime minister of the UK made him "utterly determined to prove him wrong".

The SNP likes the idea that Swinney is getting under Burnham's skin. He was after all the only contemporary political opponent the PM bothered to mention in his Liverpool address.

This is the sort of thing that might encourage some SNP members impatient for progress on independence.

Thirdly, the way in which Andy Burnham has reopened the Brexit conversation and the potential for a vote on rejoining the EU at some point has given the SNP another opening.

As they see it, if Burnham is willing to contemplate revisiting that constitutional question, it would be inconsistent for him to keep refusing Scottish voters another chance to decide on independence.

That is not the only Brexit dimension. By championing closer ties with the EU, the prime minister hopes to deliver better trading terms for Scottish businesses and perhaps make Labour more attractive to those Scots who backed "remain".

There could be dangers in that for the SNP, which has argued that independence is the best way back into the EU.

At this conference, the SNP leadership wants to shift debate from the process of achieving independence to the reasons for achieving it. That's to be backed up with a new campaign.

Swinney will also want to convince his party that he is working as hard as he can for another referendum by 2031.

His best efforts may still go unrewarded because he requires the consent of the UK government, which has been persistently withheld.

The Scottish Labour leader Michael Marra has suggested Swinney needs to demonstrate overwhelming and sustained public support for independence to secure another vote.

Opinion polls suggest the public is split down the middle on the question of Scottish statehood and that another referendum is not a high priority at a time when people are struggling with the cost of living.

Swinney has tended to the view that performing well in devolved government and delivering better public services is the best route to increasing demand for independence.

The trouble with that approach is there are plenty of examples of underperformance by the SNP in power.

Ministers are struggling to clear the post-covid backlog in the NHS, there are record numbers of homeless people in temporary accommodation, and there's been a big spike in drug-related deaths.

None of these problems are on the SNP's conference agenda, which is dominated by constitutional issues.

Swinney recently teamed up with the first ministers of Wales and Northern Ireland - all of them for the first time from nationalist parties - to push for constitutional change.

Andy Burnham has the opportunity to give a considered response this week, during what will be his first substantive visit to Scotland since taking office.

The timing - coinciding with the SNP conference - is surely not an accident. It appears purposeful, if not provocative.

The SNP responded with humour by inviting Burnham to join them in Aberdeen to agree a legal path to another referendum.

That is not going to happen. But the SNP know that any prime minister has the power to say and do things that could easily overshadow their conference discussions. It's not clear if Andy Burnham has any major announcements up his sleeve.

The BBC understands decisions on whether or not to give the go ahead for oil and gas extraction from the Rosebank and Jackdaw fields are unlikely to coincide with his visit Instead, the PM is expected to be in North Lanarkshire, discussing his plans for transferring more power from central governments to local areas.

He believes that delivering economic benefit for Scotland and "rewiring" the UK into a more decentralised state could offer an attractive alternative to independence.

Local devolution is a policy area where there is scope for some common purpose between the Holyrood and Westminster governments. Both have said they are willing to work together on pushing power into city regions and local communities. But Swinney is warning the Westminster leader not to overstep.

On day one of the SNP conference the FM told BBC Radio Scotland's Breakfast programme about a July meeting with the newly appointed PM in which Burnham committed to not legislating "over the heads of the Scottish Parliament".

Months on from that summer get-together Swinney's approach remains firm: "I intend to hold him [Burnham] to that because I think if he was to do that [bypass the Scottish Parliament], well that would be a completely unacceptable approach for the PM to take." The Scottish government is proposing a major overhaul of local government while rejecting the idea of metropolitan mayors, who already operate in parts of England like Greater Manchester.

These changes are in part designed to save money by cutting jobs and bureaucracy to help avoid a £5bn gap in devolved public spending by the end of this parliament.

There is no obvious slot on the main SNP conference agenda for these plans to be debated.

There is, however, a Saturday session just before John Swinney's speech where the Scottish Green party's co-leader Gillian MacKay has been invited to take part in a panel discussion on independence.

That may irritate some of those in the SNP who disagree with the Greens on the politics of energy, gender, and the economy.

The SNP leadership wants to show that it is comfortable with the idea that their party does not have the only pro-independence voice in the debate.

They must also remember that those like Andy Burnham, who favour continued union, also have a voice and the opportunity to influence public opinion.