A multipurpose Hopf deformation of the Algebra of Feynman-like Diagrams

We construct a three parameter deformation of the Hopf algebra $mathbf{LDIAG}$. This new algebra is a true Hopf deformation which reduces to $mathbf{LDIAG}$ on one hand and to $mathbf{MQSym}$ on the other, relating $mathbf{LDIAG}$ to other Hopf algebras of interest in contemporary physics. Further, its product law reproduces that of the algebra of polyzeta functions.