  We study conservative partially hyperbolic diffeomorphisms in hyperbolic
3-manifolds. We show that they are always accessible and deduce as a result
that every conservative $C^{1+}$ partially hyperbolic in a hyperbolic
3-manifold must be ergodic, giving an afirmative answer to a conjecture of
Hertz-Hertz-Ures in the context of hyperbolic 3-manifolds. Some of the
intermediary steps are also done for general partially hyperbolic
diffeomorphisms homotopic to the identity.
