  We write a 3D equation for three fermions by combining the three two-body
potentials obtained by the reductions of the corresponding two-fermion
Bethe-Salpeter equations to equivalent 3D equations, putting the spectator
fermion on the mass shell. In this way, the cluster-separated limits are still
exact, and the Lorentz invariance / cluster separability requirement is
automatically satisfied, provided no supplementary approximation, like the Born
approximation, is made. The use of positive free-energy projectors in the
chosen reductions of the two-fermion Bethe-Salpeter equations prevents
continuum dissolution in our 3D three-fermion equation. The potentials are
hermitian and depend only slowly on the total three-fermion energy. The one
high-mass limits are approximately exact. In view of a possible perturbation
calculation, correcting the remaining discrepancies with the three-fermion
Bethe-Salpeter equation, we succeeded in deriving our 3D equation from an
approximation of the three-fermion Bethe-Salpeter equation, in which the
three-body kernel is neglected and the two-body kernels approached by
positive-energy instantaneous expressions, with the spectator fermion on the
mass shell. The neglected terms are transformed into corrections to the 3D
equation. A comparison is made with Gross' spectator model.
