We present the results of calculations for e +H2+ scattering in the region below the first excited state. We employ three distinct and independent methods, close-coupling linear algebraic, effectiveoptical-potential linear algebraic, and R matrix, to examine the collision at the highest level of sophistication and to provide a valuable check on the results of a single technique. For the 'II"and 'II"symmetries, we find strong interference effects between various autoionizing series, leading to significant variations of the resonance width with internuclear separation R. Such variations may have profound effects on such processes as photoionization, dissociation, and recombination. For the 'Hg and 'IIg symmetries, we observe monotonic behavior of the width with R and find no evidence of strong interference effects or rapid changes.PACS number(s): 34.80.Gs