We give a method for constructing many pairs of distinct knots $K_0$ and$K_1$ such that the two 4-manifolds obtained by attaching a 2-handle to $B^4$along $K_i$ with framing zero are diffeomorphic. We use the d-invariants ofHeegaard Floer homology to obstruct the smooth concordance of some of these$K_0$ and $K_1$, thereby disproving a conjecture of Abe in [Abe16]. As aconsequence, we obtain a proof that there exist patterns $P$ in solid tori suchthat $P(K)$ is not always concordant to $P(U) \# K$ and yet whose action on thesmooth concordance group is invertible.
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