Everything shown so far for creating a push-button animation can be repeated for a door-open animation, which may be launched using a trigger. Consider the following screenshot, with a complete Mecanim graph for a door. It features an Idle state (door closed), and this transitions to a door-open animation, activated by the OpenDoor trigger.
The door-open graph can be tested, much like the push-button graph. Just select the door object in the Scene or Hierarchy panel, play the game, and then click on the Door Open trigger in the Parameters panel of the Animator window. The door should open in response.