  We consider certain invariants of links in 3-manifolds, obtained by a
specialization of the Turaev-Viro invariants of 3-manifolds, that we call
colored Turaev-Viro invariants. Their construction is based on a presentation
of a pair (M,L), where M is a closed oriented 3-manifold and L is an oriented
link in M, by a triangulation of M such that each component of L is an edge. We
analyze some basic properties of these invariants, including the behavior under
connected sums of pairs away and along links. These properties allow us to
provide examples of links in the three-sphere having the same HOMFLY polynomial
and the same Kauffman polynomial but distinct Turaev-Viro invariants, and
similar examples for the Alexander polynomial. We also investigate the
relations between the Turaev-Viro invariants of (M,L) and those of the
complement of L in M, showing that they are sometimes but not always determined
by each other.
