  In this paper, we compare two definitions of Rauzy classes. The first one was
introduced by Rauzy and was in particular used by Veech to prove the ergodicity
of the Teichm\"uller flow. The second one is more recent and uses a "labeling"
of the underlying intervals, and was used in the proof of some recent major
results about the Teichm\"uller flow. The Rauzy diagrams obtained from the
second definition are coverings of the initial ones. In this paper, we give a
formula that gives the degree of this covering. This formula is related to
moduli spaces of "framed" translation surfaces, which corresponds to surfaces
where we label horizontal separatrices on the surface. We compute the number of
connected component of these natural coverings of the moduli spaces of
translation surfaces. Delecroix proved recently a recursive formula for the
cardinality of the (reduced) Rauzy classes. Therefore, we also obtain a formula
for labeled Rauzy classes.
