Using a systematic broad-band search technique, we have carried out a survey for large Lya nebulae (or Lya blobs) at 2<z<3 within 8.5 square degrees of the NOAO Deep Wide-Field Survey (NDWFS) Bootes field, corresponding to a total survey comoving volume of ~10^8 h_70^-3 Mpc^3. Here, we present our spectroscopic observations of candidate giant Lya nebulae. Of 26 candidates targeted, 5 were confirmed to have Lya emission at 1.7<z<2.7, four of which were new discoveries. The confirmed Lya nebulae span a range of Lya equivalent widths, colors, sizes, and line ratios, and most show spatially-extended continuum emission. The remaining candidates did not reveal any strong emission lines, but instead exhibit featureless, diffuse, blue continuum spectra. Their nature remains mysterious, but we speculate that some of these might be Lya nebulae lying within the redshift desert (i.e., 1.2<z<1.6). Our spectroscopic follow-up confirms the power of using deep broad-band imaging to search for the bright end of the Lya nebula population across enormous comoving volumes.