Given a countable model M of (a large fragment of) ZFC and a forcing poset in M, we say that two generic filters over M are equivalent if they produce the same generic extensions of M. This class of Countable Borel Equivalence Relations (CBERs) was first studied by Ian Smythe (2018). Many questions about which dynamical properties (e.g., hyperfiniteness, amenability) hold for CBERs in this class remain open. A particularly interesting open problem deals with whether this equivalence for Cohen generics is hyperfinite. It was shown by Smythe (2018) that such relation is a countable increasing union of hyperfinite CBERs. In the first half of this talk we will briefly discuss what is known about this class of CBERs in general and for particular forcing notions. In the second half we will prove that this equivalence of Cohen generics is hyperfinite on the set of Cohen generics that are mutually generic to a generic collapsing the continuum. The proof will involve Borel combinatorial arguments and avoid the generic hyperfiniteness theorem.