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We consider perturbations of CR structures which preserve the complex tangentbundle. For a compact generic CR manifold its concavity properties and hencethe finiteness of some $\overline\partial_b$-cohomology groups are alsopreserved by such perturbations of the CR structure. Here we study thestability of the vanishing of these groups.

Stability of the vanishing of the $\overline\partial_b$-cohomology under  small horizontal perturbations of the CR structure in compact abstract  q-concave CR manifolds