Covariant equations and resonance states of two-particle systems with $\delta$-function potentials

The complex resonance energy (rapidity) spectra of relativistic two particle systems are found on the basis of exact solutions of the covariant two-particle equations with $\delta$-function potential and a superposition of two $\delta$-function potentials. It is established that the exact partial two particle relativistic amplitudes have resonance behavior precisely at those energy (rapidity) values, which correspond to the real part of the complex resonance energies.