  We investigate the plausibility of some models emerging from an algorithm
devised to generate a one-parameter family of interior solutions for the
Einstein equations. It is explored how their physical variables change as the
family-parameter varies. The models studied correspond to anisotropic spherical
matter configurations having a non local equation of state. This particular
type of equation of state with no causality problems provides, at a given
point, the radial pressure not only as a function of the density but as a
functional of the enclosed matter distribution. We have found that there are
several model-independent tendencies as the parameter increases: the equation
of state tends to be stiffer and the total mass becomes half of its external
radius. Profiting from the concept of cracking of materials in General
Relativity, we obtain that those models become more stable as the family
parameter increases.
