What are the visa types (H1b, L1b, H4, L2, J1, etc) accepted by TSA to learn flying for recreational purposes?

UPDATE 1
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I found some further information from [National association of flight instructors](http://www.nafinet.org/news.aspx?id=370), According to them; Person on work visa can follow Part 61 course and get the PPL.

UPDATE 2
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I have received the permission from the TSA to flow the Category 3 flight training. It took around 1 & 1/2 weeks to process and it will cost around 130 for the application and 99 for fingerprint process.

Based on this process, I understood that L1 Or L2 Or H1 Or H4 holders are eligible with the right set of document and no criminal record.