When I integrate the product of two DiracDelta functions, I get a single DiracDelta, i.e.,

Integrate[DiracDelta[x-y] DiracDelta[x-z],{x,-Infinity,Infinity}] = DiracDelta[y-z]

as expected.

However, sometimes the integral of a product of DiracDelta functions does not give the correct result. For instance one would expect:

Integrate[DiracDelta[u+z(1-x)] DiracDelta[v-z y], {z,-Infinity,Infinity}] = DiracDelta[v(1-x)+u y]

but instead gets a convergence error:

"Integral of ... does not converge on {-infinity, infinity}".

The strange thing is, if you write this integral changing $x \to 1-x$, then you get the expected result:

Integrate[DiracDelta[u+z x] DiracDelta[v-z y], {z,-Infinity,Infinity}] = DiracDelta[v x+u y]

What's going on?