We perform the first global and unitary analysis of e+e− → b ̄b cross sections. We analyze exclusive cross sections in the BB ̄, B∗B ̄(+c.c.), B∗B ̄∗, Bs∗B ̄s∗, Υ(nS)π+π− and hb(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.