It does in fact depend on internet connectivity, because it uploads all flows to the cloud. It doesn't really store anything locally on the machine, apart from some temporary local cache. It uploads the flow definition to the cloud every time you save, and it downloads it every time you want to edit your flow, or run it.
So, it depends heavily on the internet connectivity and the size and complexity of your flow - the larger your flow is (especially when it comes to UI interaction or images), the longer it takes to upload/download it.
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