An action potential releases neurotransmitter from a neuron by opening which channels?

Calcium channels.

Explanation:

The arrival of action potential at the presynaptic neuron, cause the opening of Ca + channels, at the presynpatic neuron membranes. This leads to influx of Ca+. The latter caused the Acetycholine contained vesicles in the presynaptic neuron to migrate to the tip of the presynaptic neurons, and fused with the neuronal membrane to empty their contents into the synaptic cleft.