Reference for an easy lemma on homeomorphisms of connected manifolds If M is a connected manifold of dimension $\geq 2$ then the set of orientation preserving homeomorphisms of M that are isotopic to the identity acts $n$-transitively on M for all positive $n\in\mathbb{N}$. I know several ways to prove this. I do not want to include a proof of this well known fact in my article, instead I am looking for a reference to a book or article where this is stated and proved (preferentially in a style that is not discouraging for the reader). Up to now I have not found such a reference.
Actually I only need it for dimension 2 so if your ref only covers dimension 2, I'll be happy with that.
 A: In [Ancel and Bellamy, On homogeneous locally conical spaces, Fund. Math. 241 (2018), no. 1, 1–15] it is shown that every homogeneous locally conical connected separable metric space that is not a $1$-manifold is strongly $n$-homogeneous for each $n\ge 2$.
Locally conical means that each point has a neighborhood homeomorphic to an open cone over a compact space. Manifolds are of course locally conical. It is a good elementary exercise that connected manifolds are homogeneous. (Hint: first prove it for points in the same chart, and then note that any two points can be joined by a chain of charts).
A: I suppose we induct on $n$ (the number of points) and appeal to some version of "Guggenheim's theorem".  I started by looking in "Introduction to piecewise linear topology" by Rourke and Sanderson [1982] (see page 56 and after).  In their references, I found "Extending piecewise-linear isotopies" by Hudson [1966] who in turn points at "Unpublished  doctoral  dissertation" by Irwin [1962].
Anyway, Hudson gives the result in codimension three (too bad!) but gives a complicated sufficient condition ("allowable locally unknotted") in codimension two (your situation).  But I am sure that "a finite set of points in a surface" satisfy the condition...
A: I think the following discussion (which includes references) may be interesting:
https://lamington.wordpress.com/2014/11/07/explosions-now-in-glorious-2d/
