  The particle exchange model of hadron interactions can be used to describe
three-body scattering under the isobar assumption. In this study we start from
the 3->3 scattering amplitude for spinless particles, which contains an
isobar-spectator scattering amplitude. Using a Bethe-Salpeter Ansatz for the
latter, we derive a relativistic three-dimensional scattering equation that
manifestly fulfills three-body unitarity and two-body unitarity for the
sub-amplitudes. This property holds for energies above breakup and also in the
presence of resonances in the sub-amplitudes.
