The Borel complexity of von Neumann equivalence

We prove that for a countable discrete group Γ containing copy of the free Fn, some 2≤n≤∞, as normal subgroup, equivalence relations conjugacy, orbit and von Neumann ergodic a.e. probability measure preserving actions are analytic non-Borel in Polish space Γ-actions. As consequence we obtain isomorphism spaces separably acting factors type II1, II∞ IIIλ, 0≤λ≤1, not Borel when these given Effros structure.