  The one-dimensional p-wave topological superconductor model with
open-boundary conditions is examined in its topological phase. Using the
eigenbasis of the non-interacting system I show that, provided the interactions
are local and do not result in a closing of the gap, then even and odd parity
sectors are unitarily equivalent. Following on from this, it is possible to
define two many-body operators that connect each state in one sector with a
degenerate counterpart in the sector with opposite parity. This result applies
to all states in the system and therefore establishes, for a long enough wire,
that all even-odd eigenpairs remain essentially degenerate in the presence of
local interactions. Building on this observation I then set out a full
definition of the related many-body Majorana operators and point out that their
structure cannot be fully revealed using cross-correlation data obtained from
the ground state manifold alone. Although all results are formulated in the
context of the 1-dimensional p-wave model, I argue why they should also apply
to more realistic realisations (e.g. the multi-channel p-wave wire and
proximity coupled models) of topological superconductivity.
