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Most articles show the plural form of equivalence as equivalences. The wikipedia on logical equivalence uses this form.

However, I feel like I have seen equivalencies used in contexts like mathematics as well, like in this paper Equivalencies in Mathematical Structures: An Exploration through Model Theory and Groups

Is the choice region specific (American vs European), domain specific (mathematics versus general conversation or other technical fields), or just whatever the writers preferred?

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    See Equivalence vs. equivalency. I see nothing in the full OED to suggest that the (much rarer) abstract noun form equivalency is particularly associated with mathematics. But mathematicians aren't necessarily great at natural language, so perhaps that particular "faux pas" really does occur more often in their field. But not with some "domain-specific" different meaning, I think.
    – FumbleFingers
    Aug 28 at 13:58
  • The pronunciation of equivalences and equivalencies is very similar (it might be the same in some cases, if you're not stressing the last syllable), so it's not surprising people get confused. Similarly the names Davis and Davies are constantly confused. But this can be solved with the aid of a dictionary to decide which meaning you want, or you can ask on one of the Mathematics SE sites if you are still unsure about mathematical terminology.
    – Stuart F
    Aug 28 at 14:31

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As MW notes, "equivalence" (plural "equivalences") and "equivalency" (plural "equivalencies") are synonyms in this context. According to Ngram, "equivalence" is much more common regardless of dialect.

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