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Khuri-Treiman equations have proven to be a useful theoretical tool in theanalysis of 3-body decays, specially into the $3\pi$ final state. In this workwe present in full detail the necessary generalization of the formalism tostudy the decays of particles with arbitrary spin, parity, and chargeconjugation. To this extent, we find it most convenient to work with helicityamplitudes instead of the so-called invariant amplitudes, specially whendealing with the unitarity relations. The isobar expansions in the threepossible ($s$-, $t$-, and $u$-) final channels are related with the appropriatecrossing matrices. We pay special attention to the kinematical singularitiesand constraints of the helicity amplitudes, showing that these can be derivedby means of the crossing matrix.

Khuri-Treiman equations for $3\pi$ decays of particles with spin