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Here is the fastest DT rush in Heart of the Swarm using a Warp Prism. Timing is 6:40 (when Shrine is done).
Warp Gate is normally somewhere in enemy base.

http://www.youtube.com/watch?v=aO4m0iHKPOY

Here is the same build but being rushed before I was ready.

You can also view it on youtube:
http://www.youtube.com/watch?v=PwvLRIbCrdU