We propose in this work a new method to construct the Turaev-Viro state sum
s, using a diagrammatic presentation describing surgery operation as Heegaa
rd splittings. The resulting invariants can be connected with suitable 3nj
symbols, and we evaluate them for the lens spaces. (C) 2000 American Instit
ute of Physics. [S0022-2488(00)03605-7].