  Khuri-Treiman equations have proven to be a useful theoretical tool in the
analysis of 3-body decays, specially into the $3\pi$ final state. In this work
we present in full detail the necessary generalization of the formalism to
study the decays of particles with arbitrary spin, parity, and charge
conjugation. To this extent, we find it most convenient to work with helicity
amplitudes instead of the so-called invariant amplitudes, specially when
dealing with the unitarity relations. The isobar expansions in the three
possible ($s$-, $t$-, and $u$-) final channels are related with the appropriate
crossing matrices. We pay special attention to the kinematical singularities
and constraints of the helicity amplitudes, showing that these can be derived
by means of the crossing matrix.
