Today I learned, a domain transfer can take somewhere between 1-7 days after you have entered the AUTH code for transfer. The old registerar can ask you to cancel the transfer via email but if it is left and no action for approval. So It may take somewhere between 1-7 days for actual transfer to take place depending upon registrar.
We may also have to pay for the fees for domain transfer for new registrar to accept the transfer. This also depends upon registrar and their plans/pricings.