Isomorphism and weak conjugacy of free bernoulli subflows

We show that for G a countable group which is not locally finite, the isomorphism of free G-subflows is bi-reducible with with the universal countable Borel equivalence relation E_∞, a result obtained independently by Gao-Jackson-Seward. We also show that the same result holds for the relation of weak conjugacy and for any intermediate Borel equivalence relation.