The application of diagrammatic reasoning techniques to large-scale quantum processes needs specific tools to describe families of diagrams of arbitrary size. For now, large-scale diagrammatic reasoning tools in ZH-calculus come in two flavours, !-boxes and scalable notations. This paper investigates the interactions between the two approaches by exhibiting correspondences through various examples from the literature, focusing on (hyper)graph states and diagrammatic transforms. In doing so, we set up a path toward a neat and tidy large-scale diagrammatic reasoning toolbox.Large-scale quantum diagrammatic reasoning tools tations are also well-suited for graphical transforms. Relying on this, we give alternative proofs of the spider nest identities of [25,6] by direct transform computation.Structure of the paper: We first ZH-calculus is introduced in its well-tempered form [4] in Section 1. Once both frameworks, namely !-boxes and SZH-calculus, are defined in Section 2, we describe heuristics to translate between the two in section 3. We then give concrete examples of applications of those heuristics to the hyper local complementation and regular hyper pivot [23]. Finally, in Section 4, we introduce graphical transforms in SZH-calculus and use them to derive the Fourier hyper pivot [23] and spider nest identities [25,6].
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