Careful with that assumption.
There are two "US-centric" versions -- one will work with Verizon but the other will not.
The one that WILL run on Verizon is missing LTE bands 8, 17, 19, 25, and 26.
Unfortunately AT&T actively uses 17 and Sprint uses 25, 26 (and 41). Since Sprint ALSO uses CDMA this means there is no Sprint compatibility that's worthwhile.
Band 17 is AT&Ts extended range LTE, similar to T-Mobile's Band 12. Missing it will suck if you're on AT&T and in other-than-major-metro areas it is the LTE band on AT&T. Without it you're going to fall back a LOT and your service will be severely compromised.
Both T-Mobile and AT&T actively use LTE Bands 2 & 4 (in a LOT of places), as does Verizon -- those are both relatively high-frequency bands and thus well-suited for higher-density, shorter-range tower locations (where population density is higher.)
Therefore you must choose what you want interchange with as (at least right now) T-Mobile will work perfectly well with either, but your option is to be fully operable either on AT&T OR Verizon, but not both.