  We study the singular limit of a spatially inhomogeneous and anisotropic
reaction-diffusion equation. We use a Finsler metric related to the anisotropic
diffusion term and work in relative geometry. We prove a weak comparison
principle and perform an analysis of both the generation and the motion of
interfaces. The limit problem involves motion by anisotropic mean curvature. We
also prove an optimal estimate of the thickness of the transition layer.
