Will US GSM phone work with an international (Mexico) SIM card?

I'm looking for a BLU phone, and the US GSM on amazon is $50 cheaper than the Global GSM, but I won't use it with an american company, I'd use it with a Mexican SIM card.
Since I won't need international 3G (which seems to be the problem) I'd just use it in Mexico with a Mexican SIM card and company, would it make any difference?
Do I need to get the 'Global GSM' to use it with a company from here?
Thanks

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