We perform the first global and unitary analysis of e + e − → b b cross sections. We analyze exclusive cross sections in the B B, B * B(+c.c.), B * B * , B * s B * s , Υ(nS)π + π − and h b (nP )π + π − channels as well as the total inclusive cross section for b b production. Pole positions and residues are determined for four vector states, which we associate with the Υ(4S), Υ(10750), Υ(5S) (or Υ(10860)), and Υ(6S) (or Υ(11020)). We find strong evidence for the new Υ(10750) recently claimed by Belle, although with parameters not well constrained by the data. Results presented here cast doubt on the validity of branching ratios reported earlier using Breit-Wigner parameterizations or ratios of cross sections. We also compare our results with a selection of theoretical calculations for the vector bottomonium spectrum.