In this paper, we show that any two even triangulations on the same closed surface with the same and sufficiently large number of vertices can be transformed into each other by a sequence of two specifically defined deformations called an N-flip and a P2-flip, up to homeomorphism, if they have the same homological structure. © 2008 Elsevier Inc. All rights reserved.
Kawarabayashi, K. ichi, Nakamoto, A., & Suzuki, Y. (2009). N-flips in even triangulations on surfaces. Journal of Combinatorial Theory. Series B, 99(1), 229–246. https://doi.org/10.1016/j.jctb.2008.06.006