  Given a $C^2$- Anosov diffemorphism $f: M \rightarrow M,$ we prove that the
jacobian condition $Jf^n(p) = 1,$ for every point $p$ such that $f^n(p) = p,$
implies transitivity. As application in the celebrated theory of
Sinai-Ruelle-Bowen, this result allows us to state a classical theorem of
Livsic-Sinai without directly assuming transitivity as a general hypothesis. A
special consequence of our result is that every $C^2$-Anosov diffeomorphism,
for which every point is regular, is indeed transitive.
