I have h1B if I want to transit through USA , Can I travel with B1?


I am working in Caribean countries and i have 10 years valid B1/ B2 visa. Recently i got H1B visa. i have to join my company on Jan 2015 onwards. but meanwhile i have to go back to india after my notice period in caribean country.

Now if i am travel thru USA to India, will they allow me to B1/B2 or H1B? If they allow me with H1B, will it be any problem when i enter on Jan 2015 with h1B?

Kind regards