The expression "up to (a) natural equivalence" is typical in mathematics and means roughly that we consider objects to be the same under certain conditions. (For example, when you look at someones face at different moments you see different pictures, but you know that the face that you observe is the same).
I've noticed, however, that mathematicians use both "up to natural equivalence" and "up to a natural equivalence". It seems to me that there is no difference in the meaning. It is true that both phrases are grammatically correct? It is possible to put this into some wider context?