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Gordon and Litherland showed that all compact, unoriented, possibly non-orientable surfaces in $S^3$ bounded by a link are realted by attaching/deleting tubes and half twisted bands. In this note we give an elementary proof for this result.

AN ELEMENTARY PROOF FOR THAT ALL UNORIENTED SPANNING SURFACES OF A LINK ARE RELATED BY ATTACHING/DELETING TUBES AND MÖBIUS BANDS