  We discuss the shape resonance in the superconducting gaps of a two band
superconductor by tuning the chemical potential at a Lifshitz transition for
Femi surface neck collapsing and for spot appearing. The high temperature
superconducting scenario for complex matter shows the coexistence of a first
BCS condensate made of Cooper pairs in the first band and a second boson-like
condensate made of bosons like bipolarons, in the second band where the
chemical potential is tuned near a Lifshitz transition. The interband coupling
controls the shape resonance in the pair exchange between the two condensates.
We discuss the particular BCS-Bose crossover that occurs at the shape resonance
tuning the Lifshitz parameter (the energy difference between the chemical
potential and the Lifshitz topological transition) like tuning the external
magnetic field for the Feshbach resonances in ultracold gases. This
superconducting phase provides a particular case of topological
superconductivity with multiple condensates of different winding numbers
