  For an endomorphism it is known that if all the points in the manifold have
dense sets of pre-images then the dynamical system is transitive. The inverse
has been shown for a residual set of points but the the exact inverse has not
yet been investigated before. Here we are going to show that under some
conditions it is true for Anosov endomorphisms on closed manifolds, by using
the fact that Anosov endomorphisms are covering maps.
