The transition word or phrase that would go at the beginning of the second sentence to show how the ideas are connected is "eventually". To determine this, we can look for a word or phrase that indicates a progression or change in the situation. In this case, the first sentence introduces the context of Mike begging his parents for a cell phone, and the second sentence indicates that his parents agreed to let him use his allowance to buy one. The word "eventually" implies that there was a process or progression that led to this agreement.
