The ability of large language models (LLMs) to reason effectively is crucial for a wide range of applications, from complex decision-making to scientific research. However, it remains unclear how well reasoning capabilities are transferred or preserved when LLMs undergo Knowledge Distillation (KD), a process that typically reduces model size while attempting to retain performance. In this study, we explore the effects of model distillation on the reasoning abilities of various reasoning language models (RLMs). We introduce Cognitive Flow, a novel framework that systematically extracts meaning and map states in Chain-of-Thought (CoT) processes, offering new insights on model reasoning and enabling quantitative comparisons across RLMs. Using this framework, we investigate the impact of KD on CoTs produced by RLMs. We target DeepSeek-R1-671B and its distilled 70B, 32B and 14B versions, as well as QwenQwQ-32B from the Qwen series. We evaluate the models on three subsets of mathematical reasoning tasks with varying complexity from the MMLU benchmark. Our findings demonstrate that while distillation can effectively replicate a similar reasoning style under specific conditions, it struggles with simpler problems, revealing a significant divergence in the observable thought process and a potential limitation in the transfer of a robust and adaptable problem-solving capability.