<p>Unsupervised domain adaptation has emerged as an effective paradigm to address the domain shift issue in deep neural networks. Despite its success, achieving fully supervised performance remains a potential challenge. Recent efforts have introduced active learning to the domain adaptation problem, leveraging limited manual annotation costs to achieve near fully-supervised results. However, current methods still give rise to two main concerns: (1) annotation budget: existing methods tend to label excessive redundant regions within objects, potentially resulting in a waste of the annotation budget. (2) acquisition strategy: existing methods struggle to efficiently select representative samples, which could impede the network from learning information exclusive to the target domain. In light of these concerns, we propose a novel Slide-Window-Based Active Domain Adaptation (SWADA) method for cross-modality medical image segmentation. SWADA employs a slide-window mechanism to comprehensively explore the dependencies among different window regions, preventing redundant region selections and omissions of object boundaries. This ultimately minimizes the wastage of the annotation budget. Further, we present an innovative acquisition strategy that dynamically selects windows for annotation by considering inconsistency, uncertainty, and diversity. This guarantees the representative nature of the selected window regions, consequently enhancing the performance of cross-modality segmentation. Alongside this, we propose an inter-class distance optimization strategy to model and optimize the explicit category dependencies among various objects, strengthening the feature discriminability between different categories. Extensive empirical evidence demonstrates that SWADA consistently outperforms state-of-the-art methods across three public benchmarks.</p>