The Mac and the PC need to see the correct formatting on the thumb drive to be able to use it. I'm guessing when you erased it you formatted it with a format that was incompatible with your Windows PC.
To fix it, just put the thumb drive in your Mac and erase it with GPT partitioning and exFat formatting, then the drive will work on both your Mac and your PC.
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Making mirrors is a job I can really see myself doing. 
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