Travis Kelce got downright emotional Saturday night at Taylor Swift's "Eras" tour in Amsterdam, as TS rolled out a song she hasn't sung much lately ... but seems to reflect on their relationship.

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Taylor Performed "Mary's Song (Oh My My My)," which contains the lyrics ... "I'll be 87; you'll be 89, I'll still look at you like the stars that shine, In the sky, oh my my my."

Travis got emotional, appearing to tear up and wipe his face.

"Mary's Song" debuted in 2006 on Swift's first album, long before she ever met Travis. Though, with 87 being Travis' Chief's number and 89 signifying the year Taylor was born and her "1989" album ... fans think this may be an "invisible string."

It's not the only song directed at Taylor's BF ... of course, there's the staple, "So High School," which lots of folks think nails their relationship.

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In fact, Taylor did a mash-up with the 2 songs and "Everything Has Changed," so it seems clearly directed at Mr. Kelce.

Lots of fans think it's only a matter of time before Travis pops the question ... although who knows ... that may have already happened.