Is it permissible for the one being led in prayer (ma'mum) to begin the actions of prayer after the Imam has finished them, but before the Imam says the takbir of transition?

The preferred approach is for the congregant to delay until the Imam pronounces the 'takbir' of transition, and then follow him. This applies to both the 'takbirat al-ihram' (opening takbir) and the takbirs of transition. If the congregant hastens and acts after the Imam has finished, there is no harm in it. There is no objection to preceding or equaling the Imam in the verbal pronouncements of the prayer, as long as it is not in the 'takbirat al-ihram.'

The Hanafis are of the view that following the Imam is obligatory for obligatory acts and sunnah for sunnah acts. The Malikis, however, believe that following the Imam in acts other than the 'ihram' and 'taslim' (salutation) is not a condition for the validity of the prayer. The prayer is valid, though disliked, if the congregant equals the Imam in bowing or prostrating. It is recommended that the congregant perform these acts after the Imam.

The preponderant opinion is that there is no sin in what you asked about, but it is preferable to follow the Imam.