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We prove that desingularizations of non degenerate Poincar\'e-Einsteinmetrics with A1 singularities remain non degenerate. In principle this enablesa recursive procedure to desingularize the other Fuchsian singularities. Weillustrate this procedure by the A2 case.

Non d\'eg\'en\'erescence et singularit\'es des m\'etriques d'Einstein asymptotiquement hyperboliques en dimension 4