  We investigate the connections between tree amalgamations and
quasi-isometries. In particular, we prove that the quasi-isometry type of
multi-ended accessible quasi-transitive connected locally finite graphs is
determined by the quasi-isometry type of their one-ended factors in any of
their terminal factorisations. Our results carry over theorems of Papsoglu and
Whyte on quasi-isometries between multi-ended groups to those between
multi-ended graphs. In the end, we discuss the impact of our results to a
question of Woess.
