Question: Is it true in [neutral geometry](https://en.wikipedia.org/wiki/Absolute_geometry) that "If a line $m$ parallel to to a line $\ell$ , and line $\ell$ parallel to line $n$ then $m$ parallel to line $n$"? ' where $m\ne n$

I think that this is corrent, it's true [Poincaré disk model](https://en.wikipedia.org/wiki/Poincar%C3%A9_disk_model) and also at [euclidean plane](https://en.wikipedia.org/wiki/Euclidean_geometry)

$$n------------\\
\ell------------\\
m------------$$

Answer: 
No, it is not correct. If it were correct in neutral geometry, it would be correct in every extension of neutral geometry - including hyperbolic geometry. But the standard picture of two lines through a given point - call them $m$ and $n$ - both parallel to a third line - call it $l$ - is a counterexample.

And so I think you mis-analyzed - it cannot be true in the Poincare disk model.
[![enter image description here](https://i.stack.imgur.com/mrtk3.png)](https://i.stack.imgur.com/mrtk3.png)
Here is a counter example in Poincaré disk model.