The Rauzy-Veech-Zorich induction on the space of interval exchange maps is a renormalization procedure related to the Teichmueller geodesic flow on the moduli space of Abelian differentials.
We will present analogous maps in the case of flat surfaces with Z/2Z linear holonomy. This induction is used to study connected components of the moduli space of meromorphic quadratic differentials with at most simple poles. (joint work with C. Boissy).