  We prove a result allowing to build (transitive or non-transitive) Anosov
flows on 3-manifolds by gluing together filtrating neighborhoods of hyperbolic
sets. We give several applications; for example: 1. we build a 3-manifold
supporting both of a transitive Anosov vector field and a non-transitive Anosov
vector field; 2. for any n, we build a 3-manifold M supporting at least n
pairwise different Anosov vector fields; 3. we build transitive attractors with
prescribed entrance foliation; in particular, we construct some incoherent
transitive attractors; 4. we build a transitive Anosov vector field admitting
infinitely many pairwise non-isotopic trans- verse tori.
