On the Morse--Novikov Cohomology of blowing up complex manifolds

Inspired by the recent works of S. Rao–S. Yang–X.-D. Yang and L. Meng on the blow-up formulae for de Rham and Morse–Novikov cohomology groups, we give a new simple proof of the blow-up formula for Morse–Novikov cohomology by introducing the relative Morse–Novikov cohomology group via sheaf cohomology theory and presenting the explicit isomorphism therein.