  We propose a generalization of the concept of discretized Anosov flows that
covers a wide class of partially hyperbolic diffeomorphisms in 3-manifolds, and
that we call collapsed Anosov flows. They are related with Anosov flows via a
self orbit equivalence of the flow. We show that all the examples constructed
in a paper by Bonatti, Gogolev, Hammerlindl and the third author belong to this
class, and that it is an open and closed class among partially hyperbolic
diffeomorphisms. We provide some equivalent definitions which may be more
amenable to analysis and are useful in different situations. Conversely we
describe the class of partially hyperbolic diffeomorphisms that are collapsed
Anosov flows associated with certain types of Anosov flows.
