Theorem 5.10.3 from *Introduction to dynamical systems*, by Brin & Stuck:

Let $f:M\rightarrow M$ be an Anosov diffeomorphism. Then the following are equivalent:

$NW(f)=M$,

every unstable manifold is dense in $M$,

every stable manifold is dense in $M$

$f$ is topologically transitive,

$f$ is topologically mixing.

I want to know weather it is Ok to replace "Anosov diffeomorphism" with "Partially hyperbolic diffeomorphism" in the above theorem?

You can find the definitions of hyperbolicity and partial hyperbolicity here and here