Data structure issues with incremental Delaunay triangulation

Question

I am implementing the incremental algorithm of Delaunay triangulation with a data structure based on Faces (triangles): 3 vertex indices and 3 Neighbor indices. The issue I have is that the structure is evolving during the algorithm and there are frequent creation/removal of faces, which affect the indexing of faces. So far I have overcome this issue, avoiding removing faces: updating one and adding 2 when inserting a vertex in a triangle for example. Now I am facing the same issue when removing the faces containing the 3 i(big triangle) initialization points. It seems that I am missing an important point here, should I use a dummy face list that I would also parse when inserting and update every time a face containing an initialization point has bee modified? Or is there a more elegant way to solve that issue?