While robust map maintenance has advanced significantly, existing studies have focused on specific tasks, especially dynamic object removal or change detection. In this paper, we take a holistic view of the map maintenance problem and propose MTD-Map, a single-stage framework that handles both dynamic object removal and change detection without separate task-specific modules. MTD-Map employs an explicit representation that compactly encodes the direction and duration of occupancy transitions through Mixture Transition Distribution (MTD) modeling. We develop a recursive MTD formulation that encodes historical occupancy patterns into an augmented state to capture high-order temporal dependencies. Furthermore, a stability-driven adaptive strategy balances noise suppression with the preservation of quasi-static structures. Extensive experiments verify that MTD-Map robustly removes dynamic objects and achieves competitive change detection performance, subsequently reducing computational costs. Our project page is available at: https://taeyoung96.github.io/mtd_map/.
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