When the Straight catches up with Cheatahs, the U.K. shoegaze band is en route to a show in San Diego. It’s a homecoming gig of sorts, since bassist Dean Reid is from America’s Finest City. But the road to San Diego hasn’t been a smooth one. Because the London-headquartered group’s members come from four different countries—guitarist-vocalist James Wignall is the lone Englishman, with drummer Marc Raue hailing from Dresden, Germany, and singer-guitarist Nathan Hewitt from Edmonton—sorting out their visas was a Kafkaesque ordeal of red tape. As a result, Cheatahs had to cancel the first few shows of their current North American tour while things were sorted out.

Then, with that mess behind it, the foursome suffered a further setback when its van “imploded” somewhere near Springfield, Illinois.

“It’s been a bit of a nightmare,” Hewitt relates. “We ended up putting four new wheels on it and getting an alignment done. Then we took it somewhere else and they told us that there’s a steering pin that needs to get fixed. We still have to do that when we get to L.A., because we have to take it all the way back to New York.”

Local ’gazers should be relieved that, judging by the band’s social-media updates, things are now going smoothly, and Cheatahs are on track to play Vancouver this weekend. Fans can expect plenty of the vintage-dream-pop sound that marked the quartet’s self-titled 2014 debut. This time around, though, the group has packed a sampler into the tour van to help it pull off quirkier fare like the downtempo-electronica-tinged “Signs to Lorelei” and the motorik-grooved, loop-driven “Su-pra”.

Those tracks are among the highlights of the latest Cheatahs full-length, Mythologies, which Hewitt says was the product of a more experimental approach in the studio. “Some of the songs have about, like, 50 to 100 versions,” he says. “The one that made it on the record is just a version of that. Some of them got redone 50 times, with totally different melodies and ideas and endings and all that kind of stuff. It was kind of more like cut-and-paste-style sometimes—just whatever worked.”

The album’s title is taken from the Wignall-penned “Hey, Sen”, and is a nod to Leonard Cohen’s first poetry book, Let Us Compare Mythologies. Nor is that the only literary reference. “Murasaki”, which is partially in Japanese, was inspired both by Reid’s parents (his mom’s from Japan) and Murasaki Shikibu’s 11th-century novel The Tale of Genji.

Hewitt says he and his bandmates put just as much work into the words as into the richly layered sonics, but he acknowledges that not everyone will appreciate that, and that’s fine with him. “We try to write things that, on the first listen, work musically, and then if you want to dig deeper, there’s stuff to dig at, but you don’t need to if you don’t want to,” he notes. “So you can enjoy it on whatever level you’d like.”

That should make this Saturday’s show a feast for both the ears and the mind—provided that damn van doesn’t blow up before Cheatahs can make it past the Peace Arch.

Cheatahs play the Media Club on Saturday (November 7).