How do I measure the duration of transient from a transient analysis graph?
The duration of the transient response would be the time it takes the system to settle to a (new) equilibrium or a (new) steady state. By definition, this time is infinite.  

A more common used term  is settling time. This is the time elapsed from the application of a change of input to the time at which the output has enters and remains within a specified error band, the time after which the following equality is satisfied:
$$V_3(t)-V_{3\text{, steady state}} \leq \epsilon$$

where 
\$V_{3\text{, steady state}}\$ is the steady-state value, and \$\epsilon\$ defines the width of the error band.

The answer depends on the error band as well on which time window is considered.
One can motivate the \$V_3\$ never settles, because its state changes every 1.25 ms.
When defining an error band to 4% of the steady state value and only consider 1.249 ms after voltage source V changed state, one can defined settling time of (about) 676 &micro;s.