We apply a general technique, based on the similarity renormalization procedure introduced by Glazek and Wilson, to investigate the strong coupling expansion of the Bose-Hubbard model at half filling. This approach provides a mapping of the Bose-Hubbard model onto an XXZ spin-1/2 magnetic chain, with renormalized exchange energy J and renormalized anisotropy parameter Delta. We then exploit the analytical results available for the spin-1/2 XXZ model in a finite chain of length N to compute the correlation functions of the Bose-Hubbard model and to compare them with those obtained from the numerical density matrix renormalization group approach; the agreement is very good, even at N = 30. Our approach allows to engineer a reliable quantum magnetic analog of the Bose-Hubbard model, enabling us to show that the superfluid-charge density wave (superfluid-Mott insulator) phase transition of the Bose-Hubbard model corresponds, for Delta =1 (Delta =-1) to the spin liquid-antiferromagnet (spin liquid-ferromagnet) phase transition of the XXZ-model. [with the collaboration of P. Sodano (Università di Perugia), D. Rossini (SNS-Pisa), A. Trombettoni (SISSA)]