The paper studies triangulations of surfaces up to branched transit equivalences, proving equivalence conditions and foliations.
problem Understanding triangulations of surfaces up to branched transit equivalences.
method Analyzes triangulations of closed surfaces S with vertices V, considering branched triangulations up to b-transit equivalence generated by b-flips.
result Branched triangulations are equivalent under certain conditions, including parity of Euler-Poincare' characteristic c(S).