  In this paper we investigate the spectral and scattering theory for operators
acting on topological crystals and on their perturbations. A special attention
is paid to perturbations obtained by the addition of an infinite number of
edges, and / or by the removal of a finite number of them, but perturbations of
the underlying measures and perturbations by the addition of a multiplication
operator are also considered. The description of the nature of the spectrum of
the resulting operators, and the existence and completeness of the wave
operators are standard outcomes for these investigations.
