  The treatment of elastic final state interactions (FSI) under a symmetry
group is presented. The proposed model is based on Watson's theorem, i.e. on
symmetry properties of the S-matrix and on its unitarity. This theorem provides
an easy way to introduce rescattering effects by defining final state
interactions mixing matrices. A symmetry group fixes the structure of such
mixing matrices, and the passage from one group to another is studied (for
example, SU(2) to SU(3)). Mixings among two charmless pseudoscalar decay
product states will be systematically analyzed. Finally, these mixing matrices
will be used on quark diagram parametrizations of B and D decay amplitudes.
This will have some important consequences on the definition of quark diagrams.
It will be argued that these diagrams should not contain any FSI effects, i.e.
they should be real (except for CKM factors). FSI are then introduced at the
hadronic level, by mixing basic quark diagram topologies.
