A Petri net is assumed to be live if all the transitions inside it are live. A transition inside the initial marking of a Petri net is assumed to be live if after firing several sequence of transitions it obtains enabled.
Deadlock inside a Petri net represents a reachable state inside a Petri net while none of the transitions are enabled. Liveliness in a Petri net show absents of deadlock states. Hence, it accounts for being the more desirable property of the Petri net models.