  Using the method of Green's functions within the framework of a
Bethe-Salpeter formalism characterized by a pairwise $qq$ interaction with a 3D
support to its kernel (expressed in a Lorentz-covariant manner), the 4D BS wave
function for a system of three identical relativistic spinless quarks is
reconstructed from the corresponding 3D form which satisfies a {\it fully
connected} 3D BSE. This result is a 3-body generalization of a similar
interconnection between the 3D and 4D 2-body wave functions that had been found
earlier under identical conditions of a 3D support to the corresponding BS
kernel, using the ansatz of Covariant Instaneity for the pairwise $q\bar q$
interaction. The generalization from spinless to fermion quarks is
straightforward.
