  In this article, we carry out the flattening techniques developped in a
former work in order to ``embellish" a map between compact analytic spaces, to
describe the structure of its image, getting this way a substitute for
Chevalley's theorem in the non-archimedean setting, and finally to show that
flatness in the world of Berkovich spaces amounts to naive flatness provided
one works with local rings for the G-topology
