Comparing decompositions of Poincar\'e duality pairs

Analogues of JSJ decompositions were developed for Poincar\'e duality pairs in [19]. These decompositions depend only on the group. Our focus will be on describing the edge splittings of these decompositions more precisely. We use our results to compare these decompositions with two other closely related decompositions.
Comment: v1: 50 pages, 5 figures. v2: 50 pages, 5 figures. Several minor corrections and improvements to the exposition