  We investigate the Hurwitz action of the braid group Br_n on the n-fold
Cartesian product of Br_3 and determine some stabilisers of its Artin systems.
Our algebraic result is complemented by a geometric study of families of plane
polynomial coverings of degree 3. Together they lead to characterisations of
the set of 'paths realised by degenerations' of the polynomials as defined by
Donaldson in 'Polynomials, vanishing cycles and Floer homology'.
