  We investigate the effect of periodic and disordered distributions of pairing
centers in a one-dimensional itinerant system to obtain the microscopic
conditions required to achieve an end Majorana mode and the topological phase
diagram. Remarkably, the topological invariant can be generally expressed in
terms of the physical parameters for any pairing center configuration. Such a
fundamental relation allows us to unveil hidden local symmetries and to
identify trajectories in the parameter space that preserve the non-trivial
topological character of the ground state. We identify the phase diagram with
topologically non-trivial domains where Majorana modes are completely
unaffected by the spatial distribution of the pairing centers. These results
are general and apply to several systems where inhomogeneous perturbations
generate stable Majorana modes.
