  Let $X_1^t$ and $X_2^t$ be volume preserving Anosov flows on a 3-dimensional
manifold $M$. We prove that if $X_1^t$ and $X_2^t$ are $C^0$ conjugate then the
conjugacy is, in fact, smooth, unless $M$ is a mapping torus of an Anosov
automorphism of $\mathbb T^2$ and both flows are constant roof suspension
flows. We deduce several applications. Among them is a new result on rigidity
of Anosov diffeorphisms on $\mathbb T^2$ and a new "weighted" marked length
spectrum rigidity result for surfaces of negative curvature.
