  This paper is devoted to the construction of norm-preserving maps between
bounded cohomology groups. For a graph of groups with amenable edge groups we
construct an isometric embedding of the direct sum of the bounded cohomology of
the vertex groups in the bounded cohomology of the fundamental group of the
graph of groups. With a similar technique we prove that if (X,Y) is a pair of
CW-complexes and the fundamental group of each connected component of Y is
amenable, the isomorphism between the relative bounded cohomology of (X,Y) and
the bounded cohomology of X in degree at least 2 is isometric. As an
application we provide easy and self-contained proofs of Gromov Equivalence
Theorem and of the additivity of the simplicial volume with respect to gluings
along \pi_1-injective boundary components with amenable fundamental group.
