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There is an ArcGIS Idea that requests a Macro Recorder for Python which sounds like it may be what you are after.
If your analysis is done using the geoprocessing tools, you can open the geoprocessing results tab and see all the tools used in your session or previous sessions. I have not experimented much with it but looks like you can create python script snippets or save it to a results file (rlt.) That would be the closest thing.
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