2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112709In this paper it is proved that relative hyperbolicity is an invariant of quasi-isometry. As a byproduct of the arguments, simplified definitions of relative hyperbolicity are obtained. In particular we obtain a new definition very similar to the one of hyperbolicity, relying on the existence for every quasi-geodesic triangle of a central left coset of peripheral subgroup.34 pages, Latex; added references, corrected typos, pictures included in the Latex fileGroup TheoryGeometric Topologytext