When I have two DiracDeltas and one integral, I expect to get a single DiracDelta after the integration:

i.e.

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

which works expectedly.

However, sometimes product of a DiracDelta does not give a correct result.

For instance, you expect,

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

On the contrary from expected result, you get a convergence error: "Integral of ... does not converge on {-$\infty, \infty$}".

The strange thing is, if you write it instead with $x \to 1-x$, 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?