Those of a cynical disposition might say that, when you strip away the screens, lights, steam and explosions – and the chunky plastic bracelets every fan is given on the way in – then all you have left at a Taylor Swift concert is old-fashioned entertainment: cracking songs, a good band, and some nice dancing to set it off.

But throw in all those extras, and what you get is a modern-day masterclass in pop production and musicianship that no one with a heart could entirely resist. If you need proof, go looking for Trouble. Here, this belter of a track gets an added bolt of rock and roll raunch. Guitars chug and swagger; steams shoots into the air; the arena turns red with those light-up bracelets doing their business. And around the world a handful of very famous manchilds rue the day they crossed the Tay Tay.

You can count the hits by the costume changes, which probably go a corset or two too far, but there’s not a dull track in this set. Where the show stumbles – and you’ll not hear this from a single Swifty – is between songs. Taylor is masterful at making her fans feel involved, in concert or online. However, telling a 13,000-strong crowd that she can recognise individual faces from their posts, tweets and Taylurking online seems at best cynical and at worst manipulative. A few minutes later, she’s also warning the same crowd that sometimes online relationships are not as substantial as they can seem – luckily for her, irony doesn’t set those bracelets off or they could blow up in her beautiful face.

The oddest addition are the between-song videos. In these, Swift’s BFFs (if you have to look it up, you’re in the wrong review) bang on about how brilliant and normal she is. They also happen to be world-famous stars such as Lena Dunham, Cara Delevingne and Selena Gomez – the cringe during this gives us cramp, and as for Haim: we expect better from you.

You can, of course, disregard all of this because, as any decent Swift fan knows, haters gonna hate, hate, hate, and this is a juggernaut of a show, built around the stage's solo bridge. Swift strolls its length, strumming an acoustic guitar and getting the crowd to echo the lines of You Are In Love, before it rises up and pivots around the arena, putting her eye to eye with the first tier of screaming fans. This fine bit of bridgework is put to use for the rest of the show. On Style, her 12-strong troupe of male dancers (where are the women?) slip and slide their way along it, while the five-piece band and four backing singers pump out the pitch-perfect pop. (As a man who can watch 10 episodes of Got to Dance back-to-back, though, the choreography left a lot to be desired.) And Bad Blood gets a brilliant black and red makeover, while gleefully nicking its look from Seven Nation Army.

It all ends (where else?) in a riot of pink and neon to Shake It Off, with the dancers and Swift swinging and singing their way along that airborne gantry while tickertape tumbles from the rafters, explosions fizz along the stage, and delirious teenagers scream like their lives depend on it.

And maybe they do - this is a two-hour show of strength by the world’s biggest pop superpower. There are plenty worse causes to devote your teenage years to.

Taylor Swift plays 3Arena tonight. Sold out