Transitivity of euclidean extensions of anosov diffeomorphisms

We consider the class of R-n extensions of Anosov diffeomorphisms on infranilmanifolds, and find necessary and sufficient conditions for topological transitivity. In particular, if the fiber is R, the existence of a semi-orbit with the projection on R unbounded from above and from below is equivalent to topological transitivity. We also show that in the above class topological transitivity and stable topological transitivity are equivalent.