The universal cover of an algebra without double bypass

Let A be a basic and connected finite dimensional algebra over a field k of characteristic zero. We show that if the quiver of A has no double bypass then the fundamental group (as defined in [R. Martínez-Villa, J.A. de la Peña, The universal cover of a quiver with relations, J. Pure Appl. Algebra 30 (1983) 277–292]) of any presentation of A by quiver and relations is the quotient of the fundamental group of a privileged presentation of A. Then we show that the Galois covering of A associated with this privileged presentation satisfies a universal property with respect to the connected Galois coverings of A in a similar fashion to the universal cover of a topological space.