Covariant four-dimensional scattering equations for the NN-π NN system

We derive a set of coupled four-dimensional integral equations for the $NN-\pi NN$ system using our modified version of the Taylor method of classification-of-diagrams. These equations are covariant, obey two and three-body unitarity and contain subtraction terms which eliminate the double-counting present in some previous four-dimensional $NN-\pi NN$ equations. The equations are then recast into a from convenient for computation by grouping the subtraction terms together and obtaining a set of two-fragment scattering equations for the amplitudes of interest.