Well, it may be a case of being a little late . In GSM India uses frequencies 900/1800 , whereas US uses 850/1900. So on buying a GSM phone in US it is important to make sure that the phone you are getting supports the 900/1800 frequencies. If it supports one of the two (900 or 1800) then it may work on some providers alone.
Coming to CDMA - US uses 800/1900. India uses 800. However, in US, Mobile Number Portability exists for a long time & all you need to do is contact the new provider & do a few basic formalities and automatically your number will switch to the new provider - no need of any change in sim card etc. Hence you do not find them manufacturing individual sim cards. Any phone is likely to work on CDMA networks available in your area.
So it is likely that your phone must be supporting the 800 frequency of CDMA which is common to both India & US & hence you are able to see "Reliance".
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Well, the answer would be - contact reliance (or any other CDMA provider) and ask them, how can you switch to them . There was a time when CDMA phones in India used to come without SIM only & there was a process wherein the provider used to switch you to a newer handset. Maybe the process will still be in place.
And if you want GSM provider, I doubt you will be able to make it work. But if you do have the specs of the handset with you. See if it has 900/1800 support in it
