  We prove that the 2-category of action Lie groupoids localised in the
following three different ways yield equivalent bicategories: localising at
equivariant weak equivalences \`a la Pronk, localising using surjective
submersive equivariant weak equivalences and anafunctors \`a la Roberts, and
localising at all weak equivalences. These constructions generalise the known
case of representable orbifold groupoids. We also show that any weak
equivalence between action Lie groupoids is isomorphic to the composition of
two particularly nice forms of equivariant weak equivalences.
