Rituximab With or Without Stem Cell Transplant in Treating Patients With Minimal Residual Disease-Negative Mantle Cell Lymphoma in First Complete Remission

Inclusion Criteria: * INCLUSION CRITERIA FOR SCREENING (STEP 0 - PREREGISTRATION) * Age \>= 18 and =\< 70 years * Patients must have histologically confirmed mantle cell lymphoma, with cyclin D1 by immunohistochemical stains and/or t(11;14) by cytogenetics or fluorescence in situ hybridization (FISH). If patient has cyclin D1 negative mantle cell lymphoma with classical morphology and an expression profile (including SOX11+) that is otherwise indistinguishable from mantle cell lymphoma, communication with investigator is required for consideration of enrollment. The proliferation rate, using Ki-67 or MIB-1, should also be determined, but is not required until step 1 registration; patients may register to step 0 without a documented Ki-67 index * In the opinion of the enrolling physician, patients must be felt to be a candidate for autologous stem cell transplantation * Patient may be about to begin, be receiving or have completed induction therapy within 120 days prior to preregistration to step 0; no more than 300 days may have passed between the first day of induction therapy and preregistration to step 0 * For patients who have completed induction therapy and have been restaged, restaging evaluation must show status of partial (PR) or complete response (CR); post-induction patients with evidence of clinical disease progression are not eligible for preregistration * Up to two regimens of therapy (conventional chemotherapy, antibody therapy, or an oral regimen) are all…