  Given an Anosov vector field $X_0$, all sufficiently close vector fields also
are of Anosov type. In this note, we check that one can choose the so-called
"Faure-Sj\"ostrand" anistropic spaces to be adapted to any smooth vector field
sufficiently close to $X_0$ in $C^1$ norm. It follows that finite families of
resonances depend smoothly on the vector field with the usual caveats.
  In this second version, more details are given on the perturbation of
spectral projectors.
