Sorry for the late reply 
So, what I do is: My start animation goes from idle, to a light run, to the start of the full Run…
And the transition is: Is the character moving? Generally true when any input is used, except when they cancel each other out, like Forward + backwards at the same time. If he is moving, is the speed > 0.01? If so, enter into the Start running animation. I almost never uses a Slope on speed to blend between animations, because animations like that lack Anticipation on movements.