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Taylor Swift is giving fans their first look at her new album cover ... revealing the front and back of "The Life of a Showgirl." store.taylorswift.com

The singer-songwriter dropped the first look at the album on her website and on boyfriend Travis Kelce 's "New Heights" podcast Wednesday. Check it out ... TS is channeling her inner showgirl while underwater in a glittery, bedazzled bodysuit.

Of course, we knew Taylor showed the album on the podcast ... 'cause a promo clip from the episode showed the cover totally blurred out -- driving fans into a frenzy of wonder about the artwork.

The new album's sparking conversation among her diehard Swifties ... with some wondering if she'll throw shade at her longtime friend Blake Lively

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