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We study some comparison between a bilinear cohomology pairing in localcoefficients and the Blanchfield pairing of a knot. We show that the formerpairing is an $S$-equivalent invariant, and give a criterion to a relationbetween the two pairings. We also observe that the pairings of some knots areequivalent, and that the pairings of other knots are not equivalent.

Some comparisons of Blanchfield pairings and cohomology pairings of knots