IT'S usually the Dial-a-Bus which crawls along Kirkintilloch main street, the administrative capital of a sleepy hollow where the only sense of the political is the local hullabaloo over the controversial 'shared space' scheme rumbling across its hinterland.

On Monday the UK Liberal Democrats leader roared into town, here to champion East Dunbartonshire's prodigal daughter, its former MP Jo Swinson. While Kirkintilloch's new streetscape has caused endless confusion amongst motorists and pedestrians, Tim Farron's message from his campaign battlebus could not have been clearer: 'only Jo can stop the SNP'.

The portents are good the LibDems reckon. Swinson was considered a hard-working, diligent and personable local MP during her 10 years, particularly in her first term when the LibDems were buoyed by an anti-Iraq War sentiment and she was not saddled with membership of the UK coalition Government.

The council elections returned the best local LibDem show in a decade and they insist they will not do a localised re-run of their time in Government via an alliance with the Tories. The fact the leader is in town suggests a party belief it can pour its efforts and resources into a target areas often and deliver a result.

East Dunbartonshire delivered one of the highest Remain votes in last year's Brexit referendum. It was also one the biggest returns for No in the independence referendum two years previous. It ticks two core LibDem boxes. And crucially, with just 2000 votes in it in 2015 between Swinson and the SNP's John Nicolson, is one of the tightest margins in the country.

"Jo has instant recognition. People are just delighted to see her back", said Swinson's campaign manager Katy Gordon. "When we launched our campaign on a barge on the canal random people were shouting from the path 'good luck Jo, SNP out'.

"We've just exceeded our expectations at the council elections with an exciting new team and we're the only party which reflects the huge support for the EU and the UK in East Dunbartonshire.

"It really feels a lot like the 2014 referendum which we led on on the area. Labour and Tory voters are saying they will be backing us to stop the SNP. People didn't miss what they had with Jo and a lot of people are contrasting her with the current MP."

East Dunbartonshire is in many ways a constituency of two halves. On the west side lies the leafy old-monied suburbs of Bearsden and Milngavie. Over east are the aspirational Bishopbriggs and Lenzie, and the more traditional working class Kirkintilloch and the Campsie towns.

The SNP campaign is more focused on the eastern end. It did well here last week, returning the highest number of councillors in the constituency. And there is a sense the more traditional home of the LibDem voter in the west could be where they come undone.

In 2015, despite losing, Swinson's vote went up, a clear indication of a middle-class tactical vote when the SNP really threatened. With Tory tails up, the previous incumbent is maybe not so assured of securing all the anti-SNP votes needed to get over the line.

"It maybe be the case that a resurgent Tory vote is what does for Swinson", said a local Labour source. "I can't see them winning but it may damage the LibDems. Nicolson's vote will hold and there's no Labour threat.

"Jo's real fear should be the Tories and those who don't forgive her for sitting in the room with Osborne and Cameron when they were making decisions."

For Nicolson, any sense of a LibDem surge "is in their leaders' heads alone", describing their pitch of halting Brexit as "absurd" and believing they will be haunted by their time in Government.

"One problem they face is that the election was called too early" he said. "People have a very recent muscle memory of when the LibDems were in power and they're just not trusted. They're slippery.

"Locally they've been in cahoots for years with the Tories and Labour on any number of controversial issues. They were voting to close schools here while at the same time saying publicly they were opposed to closing them. It goes back to slipperiness."

Nicolson too has recognition. He is a regular sofa guest on network politics shows, his tone perhaps sitting easier with his constituency's demographic. He has a different recollection of the LibDem campaign launch.

"Jo and Willie Rennie re-enacted the scene from the Titanic", he says.

He adds: "Brexit is the main issue on many doorsteps and people are right to worry about it. The only reason Theresa May called this election is that the terrible Brexit deal she is going to get will be clear to everyone in two years time. She wants to be protected by a crushing Westminster majority.

What we're saying is that it's in Scotland's interests to have a strong SNP opposition at Westminster.

"With a handful of MPs the LibDems can't stop the Tory hard Brexit juggernaut so what we're saying is keep your options open. It make sense to have a parachute in case we need it. Who wants to close off their options?"