I will talk on classifying non-transitive Anosov flows on Franks-Williams manifolds. Here a Franks-Williams manifold is an irreducible 3-manifold whose JSJ pieces are two figure eight knot complement spaces. In the history, Franks and Williams firstly construct a non-transitive Anosov flow on one of this kind of manifolds. This is a joint work with Jiagang Yang.