Relatively hyperbolic groups: geometry and quasi-isometric invariance

In 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.