  Motivated by the InSb nanowire superconductor system, we investigate a system
where one-dimensional topological superconductors are placed in parallel. It
would be simulated well by a ladder of the Kitaev chains. The system undergoes
multiple topological phase transitions, where the number of Majorana fermions
changes as a function of the interchain superconducting pairings. We
analytically determine the topological phase diagram by explicitly calculating
the topological number and the band structure. They show even-odd effects with
respect to the number of legs of the ladder. When the relative phase between
the inter- and intrachain superconducting pairings is 0 or $\pi$, the system
belongs to the class BDI characterized by the $\mathbb{Z}$ index, and otherwise
it belongs to the class D characterized by the $\mathbb{Z}_2$ index. This
topological class change would be caused by applying the Josephson current or
an external magnetic field, and could be observed by measuring the zero-bias
differential conductance.
