Abstract: We provide an explicit Seifert surface algorithm for null-homologous links in closed 3-manifolds using surgery diagrams. In particular, the algorithm generates Seifert surfaces embedded in the complement of the surgery link, and we show how these surfaces can be explicitly found in examples. This yields a computable formula for the linking number of two null-homologous knots, from which the associated Seifert matrices can be read off.
