@Al ******
, what you do is you apply for a 90 day Non-Immigrant Type O <-( O meaning other) visa at the immigration office when you have 15 or more days remaining on either your 30 day visa exempt entry or your 60 day tourist visa entry. It's not transitional to anything, you're applying for a brand new visa.
After that you get the 90 day Non-O and are on the last 30 days of that stamp you can apply for the yearly extension of stay