  In this paper, we describe a new approach to the problem of classification of
transitive Anosov flows on 3-manifolds up to orbital equivalence. More
specifically, generalizing the notion of Markov partition, we introduce the
notion of Markovian family of rectangles in the bifoliated plane of an Anosov
flow. We show that any transitive Anosov flow admits infinitely many Markovian
families, each one of which can be canonically associated to a finite
collection of combinatorial objects, called geometric types. We prove that any
such geometric type describes completely the flow up to Dehn-Goodman-Fried
surgeries on a finite set of periodic orbits of the flow. As a corollary of the
previous result, we show that any Markovian family can be canonically
associated to a finite collection of combinatorial objects, called geometric
types with cycles, each describing the flow up to orbital equivalence.
