On the equivalence of standard and covariant perturbation series in non-polynomial pion lagrangian field theory

Recently a covariant perturbation approach has been developed to give a perturbation expansion of the chiral-invariant pion theory which does not depend on the choice of pion coordinates. We prove that this covariant approach is equivalent to standard perturbation theory. Our method explicitly shows how one can express covariant graphs by contributions of non-covariant ones and vice versa. We neglect contributions vanishing on the mass shell.