The application of large language models (LLMs) in the medical field has garnered significant attention, yet their reasoning capabilities in more specialized domains like anesthesiology remain underexplored. To bridge this gap, we introduce AnesSuite, the first comprehensive dataset suite specifically designed for anesthesiology reasoning in LLMs. The suite features AnesBench, an evaluation benchmark tailored to assess anesthesiology-related reasoning across three levels: factual retrieval (System 1), hybrid reasoning (System 1.x), and complex decision-making (System 2). Alongside this benchmark, the suite includes three training datasets that provide an infrastructure for continued pre-training (CPT), supervised fine-tuning (SFT), and reinforcement learning with verifiable rewards (RLVR). Leveraging this suite, we develop Morpheus, the first baseline model collection for anesthesiology reasoning. Despite undergoing limited training with SFT and group relative policy optimization (GRPO), Morpheus not only achieves substantial improvements in anesthesiology that rival larger-scale models, but also demonstrates enhanced reasoning capabilities across general medical and broad-domain benchmarks. Furthermore, through comprehensive evaluations and experiments, we analyze the key factors influencing anesthesiology reasoning performance, including model characteristics, training strategies and training data. Both AnesSuite and Morpheus will be open-sourced at https://github.com/MiliLab/AnesSuite.