Transition from Walk Left to Walk Right

I've created a 2D character and simple "Walk Left," "Walk Right," and "Idle animations. All 3 of the animations work fine, but when transitioning from either "Walk Right" to "Walk Left" or "Idle" to "Walk Left" instead of the character's body parts being instantly in place they visibly move to the position they need to be in.

Below is a video of the problem

http://youtu.be/UPD73dwpdQY?t=9s

I'm fairly new to Unity so sorry if there is a simple solution to this.

Thanks in Advance!

 

I got a similar problem some days ago.
I dont know if it's the best solution, but worked for me.
To solve this i selected the transition between the animations and changed the "transition" (i dont know how it's called) to none. So when the transition occur there is no "smoothness" on it.

Here is an image:

 

Thank you Vitor_r! That completely fixed my issue!