  We propose a procedure based on phase equivalent chains of Darboux
transformations to generate local potentials satisfying the radial
Schr\"odinger equation and sharing the same scattering data. For potentials
related by a chain of transformations an analytic expression is derived for the
Jost function. It is shown how the same system of $S$-matrix poles can be
differently distributed between poles and zeros of a Jost function which
corresponds to different potentials with equal phase shifts. The concept of
shallow and deep phase equivalent potentials is analyzed in connection with
distinct distributions of poles. It is shown that phase equivalent chains do
not violate the Levinson theorem. The method is applied to derive a shallow and
a family of deep phase equivalent potentials describing the $^1S_0$ partial
wave of the nucleon-nucleon scattering.
