  We prove that for a countable discrete group $\Gamma$ containing a copy of
the free group $\F_n$, for some $2\leq n\leq\infty$, as a normal subgroup, the
equivalence relations of conjugacy, orbit equivalence and von Neumann
equivalence of the ergodic a.e. free actions of $\Gamma$ are analytic non-Borel
equivalence relations in the Polish space of probability measure preserving
$\Gamma$ actions. As a consequence we obtain that the isomorphism relation in
the spaces of separably acting factors of type $\II_1$, $\II_\infty$ and
$\III_\lambda$, $0\leq\lambda\leq 1$, are analytic and not Borel when these
spaces are given the Effros Borel structure.
