We study possible many body phenomena in the Quantum Anomalous Hall system of weakly interacting spinor bosons in a square lattice. There are various novel spin-bond correlated superfluids and quantum or topological phase transitions among these phases. Most notably, we find an anti-unitary Reflection $ R $ symmetry protected bosonic topological phase transition (BTPT) separating two different ground states which break identical symmetries of the Hamiltonian. The two phases can only be distinguished by the different topology of the BEC condensation momenta (or bosonic zero modes) instead of any differences in the symmetry breaking patterns.
Breaking the $ R $ symmetry explicitly by a Zeeman field will transfer the BTPT to a bosonic Lifshitz transition with accompanying symmetry breakings. This could be the first bosonic analog of the fermionic topological phase transition with the associated change in the topology of the Fermi surfaces, Dirac points or Weyl points or nodal lines. However, the BTPT is interaction driven, so may be more profound than its fermionic counterpart. Finite temperature effects will also be briefly discussed. All these new many body bosonic topological phenomena can be probed in the recently experimentally realized weakly interacting Quantum Anomalous Hall (QAH) model of $ ^{87} Rb $.