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In this paper it is proved that relative hyperbolicity is an invariant ofquasi-isometry. As a byproduct of the arguments, simplified definitions ofrelative hyperbolicity are obtained. In particular we obtain a new definitionvery similar to the one of hyperbolicity, relying on the existence for everyquasi-geodesic triangle of a central left coset of peripheral subgroup

Relatively hyperbolic groups: geometry and quasi-isometric invariance