  Hadron decay chains constitute one of the main sources of information on the
QCD spectrum. We discuss the differences between several partial wave analysis
formalisms used in the literature to build the amplitudes. We match the
helicity amplitudes to the covariant tensor basis. Hereby, we pay attention to
the analytical properties of the amplitudes and separate singularities of
kinematical and dynamical nature. We study the analytical properties of the
spin-orbit (LS) formalism, and some of the covariant tensor approaches. In
particular, we explicitly build the amplitudes for the B -> psi pi K and B ->
Dbar pi pi decays, and show that the energy dependence of the covariant
approach is model dependent. We also show that the usual recursive construction
of covariant tensors explicitly violates crossing symmetry, which would lead to
different resonance parameters extracted from scattering and decay processes.
