  Although a large class of topological materials have uniformly been
identified using symmetry properties of wave functions, the past two years have
seen the rise of multi-gap topologies beyond this paradigm. Given recent
reports of unexplored features of such phases, platforms that are readily
implementable to realize them are therefore desirable. Here, we demonstrate
that multi-gap topological phase transitions of non-Abelian charged nodal lines
arise in classical phonon waves. By adopting a simple spring-mass system, we
construct nodal lines of a three-band system. The braiding process of the nodal
lines is readily performed by adjusting the spring constants. The generation
and annihilation of the nodal lines are then analyzed using Euler class.
Finally, we retrieve topological transitions from trivial nodal lines to a
nodal link. Our work provides a simple platform that can offer diverse insights
to not only theoretical but also experimental studies on multi-gap topology.
