Let $K$ be a knot in the 3-sphere $S^3$.

Here we denote by $s(K)$ Rasmussen's s-invariant for $K$, and by $X_{K}(n)$ the 4-manifold obtained from the standard 4-ball $B^4$ by attaching a $2$-handle along $K$ with framing $n$.

My question is the following.

For two knots $K$ and $K'$ such that $X_{K}(0)$ and $X_{K'}(0)$ are diffeomorphic, is it true that $s(K)=s(K')$?

I am also interested in the same question for Ozsváth-Szabó's $\tau$-invariant.

Note that it is known that there exist knots $J$ and $J'$ such that
$\partial X_{J}(0)$ and $\partial X_{J'}(0)$ are diffeomorphic,
and $s(J) \neq s(J')$, see Yasui's paper *Corks, exotic 4-manifolds and knot concordance*.