Neurotransmitters carry nerve impulses across where

Neurotransmitters don't actually carry nerve impulses across a synaptic cleft. What neurotransmitters do is they bind to the receptors that can be found on the receiving ends of a synaptic cleft (usually called postsynaptic neurons on whose receptors a neurotransmitter binds). When enough of them are bound onto neurons, they then can cause a temporary depolarization which can carry over an action potential.