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In this note we prove the relation between Betti numbers of an Arf semigroup$S$ and its blowup $S'$ in the case when they have the same multiplicity $n$.The relation is then $\beta_{i,s}(S')=\beta_{i,{s+(i+1)n}}(S)$.

On the relation between Betti numbers of an Arf semigroup and its blowup