The influence of pairing asymmetry on thermoacoustic instabilities was experimentally investigated in an odd-numbered can-annular combustion system, using 3D FEM-based Helmholtz simulation and acoustic wave decomposition method. We show that a pair of degenerate mode is split into two modes with a frequency difference of 6 Hz, which is induced by a pairing-asymmetry-related geometrical property. Interestingly, the modal interaction between splitting modes gives rise to the periodic transition between standing and spinning azimuthal instabilities in annular cross-talk section.