Unitarity flow in 2+1 dimensional massive gravity

We analyze the most general case of third-order Chern-Simons-like theories of massive 3D gravity. Results show the conditions for finding the unitary regions on the parameter space. There exists (n-1)th order theories on the boundary of a unitary nth order model on parameter space under certain conditions, as the first example recently demonstrated from the bimetric generalization of exotic massive gravity. We investigated the mechanism that causes this type of transition for third-order models. Hamiltonian analysis of the theory also presents that ghost and no-ghost regions can be separated by Chern-Simons theories.