As @MarcoGolla mentioned, the framing can be controlled due to Akbulut's carving technology: a *dotted* circle notation. It was introduced in the following article:

Akbulut, Selman. "On 2-dimensional homology classes of 4-manifolds." Mathematical Proceedings of the Cambridge Philosophical Society. Vol. 82. No. 1. Cambridge University Press, 1977.

Let $U$ be the unknot in $S^3$ and $D_U$ be the ribbon disk in $B^4$ with $\partial D_U = U$. Observe that $S^1 \times B^3$ is the ribbon disk exterior of $D_U$, i.e., it is diffeomorphic to $B^4 \setminus \nu(D_U)$ where $\nu(D_U) \approx D_U \times B^2$.

Consider a ribbon knot with a ribbon disk $(K,D) \subset (S^3,B^4)$. Similarly, one can try to understand the $4$-manifold $B^4 \setminus \nu(D)$. The procedure of the construction of the Kirby diagram was answered, for instance here.

Once it is understood, one can also put a *dot* on the ribbon disk exterior. The reference is again Akbulut's book Section 1.1 and 1.4 about carving ribbon disks:

Akbulut, Selman. 4-manifolds. Vol. 25. Oxford University Press, 2016.

It equivalently represents the ribbon disk exterior. See again Exercise 1.10 and Figure 1.22 in Akbulut's book.

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