NN-Flips in even triangulations on the projective plane

We shall show that any two even triangulations GG and G′G′ on the projective plane with |V(G)|=|V(G′)|≥14|V(G)|=|V(G′)|≥14 can be transformed into each other by two operations called an NN-flip and P2P2-flip, if and only if both of them are simultaneously 3-colorable, or not.