  We show that the family of Podles' spheres is complete under equivariant
Morita equivalence (with respect to the action of quantum SU(2)), and determine
the associated orbits. We also give explicit formulas for the actions which are
equivariantly Morita equivalent with the quantum projective plane. In both
cases, the computations are made by examining the localized spectral
decomposition of a generalized Casimir element.
