Compositional Zero-Shot Learning (CZSL) aims to recognize novel \textit{state-object} compositions by leveraging the shared knowledge of their primitive components. Despite considerable progress, effectively calibrating the bias between semantically similar multimodal representations, as well as generalizing pre-trained knowledge to novel compositional contexts, remains an enduring challenge. In this paper, our interest is to revisit the conditional transport (CT) theory and its homology to the visual-semantics interaction in CZSL and further, propose a novel Trisets Consistency Alignment framework (dubbed TsCA) that well-addresses these issues. Concretely, we utilize three distinct yet semantically homologous sets, i.e., patches, primitives, and compositions, to construct pairwise CT costs to minimize their semantic discrepancies. To further ensure the consistency transfer within these sets, we implement a cycle-consistency constraint that refines the learning by guaranteeing the feature consistency of the self-mapping during transport flow, regardless of modality. Moreover, we extend the CT plans to an open-world setting, which enables the model to effectively filter out unfeasible pairs, thereby speeding up the inference as well as increasing the accuracy. Extensive experiments are conducted to verify the effectiveness of the proposed method.