Variation of the Alexander–Conway polynomial under Dehn surgery

Let ε1 and ε2 belong to {±1}. When the ε1-surgery along a knot K1 in S3 produces the same homology sphere as the ε2-surgery along a knot K2 in S3, then the Casson surgery formula implies that ε1ΔK1″(1)=ε2ΔK2″(1), where Δ(t) denotes the symmetric Alexander polynomial. For any pair (Λ1(t),Λ2(t)) of possible knot Alexander polynomials such that ε1Λ1″(1)=ε2Λ2″(1), we exhibit a pair (K1,K2) of knots in S3 such that ΔK1(t)=Λ1(t), ΔK2(t)=Λ2(t) and the ε1-surgery along K1 produces the same homology sphere as the ε2-surgery along K2.