# What's wrong with the following Plot in Manipulate?

I try to show the convolution of a step function and a triangle function is smooth with the following code:

Manipulate[f0 = UnitBox[p - t0]; f1 = 2 UnitTriangle[t0];
f2 = Convolve[f0, f1, t0, t1];
Plot[{f0, f1, f2} /. {t0 -> x, t1 -> x}, {x, -3, 3}],
{{p, -2}, Locator}]


It should be something like this:

But after have a click to locate the Locator, it seems Mathematica have plot some "non-necessary" curves (I have marked by red cross):

How the get the right plot?

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I'm not really sure what you expect, because a Locator is clearly a point {x,y}. Even if you initialize it with -2, after the first click, it is converted to a point, thus the behavior.
Manipulate[f0 = UnitBox[First[p] - t0]; f1 = 2 UnitTriangle[t0];