variable inverting op-amp Schmidt trigger
Using a variable resistor for R3 will give a variable amount of hysteresis.  

Using a variable resistor for R1 or R2 will adjust the center point voltage (comparison voltage).  

The actual switching points of the comparator will be at a voltage which is a combination of the center point voltage and the hysteresis amount.  When the output goes high the  hysteresis increases the comparison voltage, when the output goes low the hysteresis decreases the comparison voltage.

So you could say that R1 R2 adjusts the center point of the threshold, and R3 adjusts the high-low window width of the threshold.