This paper studies on the dimensions of spline spaces over some given $T$-meshes. Using the smoothing cofactor-conformality method, we study the instability in the dimensions of the spline spaces over $T$-meshes with 2-nested and 3-nested $T$-cycles. We define a singularity factor of each simple $T$-cycle, the instability and the structure's degeneration are associated with the singularity factors. In order to get a stable dimension formula over $T$-mesh with a $N$-nested $T$-cycle, a constraint on the $T$-mesh is introduced. Finally, a possible degeneration for a case of parallel $T$-cycles is illustrated.