Causal discovery algorithms aim at untangling complex causal relationships\nfrom data. Here, we study causal discovery and inference methods based on\nstaged tree models, which can represent complex and asymmetric causal\nrelationships between categorical variables. We provide a first graphical\nrepresentation of the equivalence class of a staged tree, by looking only at a\nspecific subset of its underlying independences. We further define a new\npre-metric, inspired by the widely used structural intervention distance, to\nquantify the closeness between two staged trees in terms of their corresponding\ncausal inference statements. A simulation study highlights the efficacy of\nstaged trees in uncovering complexes, asymmetric causal relationships from\ndata, and real-world data applications illustrate their use in practical causal\nanalysis.\n