Rituximab and Combination Chemotherapy With or Without Bleomycin Sulfate in Treating Patients With Primary Mediastinal Large B-Cell Lymphoma

DISEASE CHARACTERISTICS:

* Histologically confirmed primary mediastinal (thymic) large B-cell lymphoma as defined by WHO classification of lymphoid neoplasms

  * Diagnosis must be based on an adequate tissue sample, such as an excisional biopsy or core-needle biopsy
* A paraffin-embedded block of well-fixed lymphoma tissue must be available
* Measurable disease, defined as ≥ 1 lesion that can be accurately measured in ≥ 1 dimension as ≥ 10 mm
* No active or untreated CNS lymphoma

  * A lumbar puncture is not required in the absence of neurologic symptoms

PATIENT CHARACTERISTICS:

* ECOG performance status 0-2
* ANC ≥ 1,000/mm\^3 (unless related to disease)
* Platelet count ≥ 100,000/mm\^3 (unless related to disease)
* Total bilirubin ≤ 2.0 times upper limit of normal (ULN)
* AST and/or ALT ≤ 2.5 times ULN
* Creatinine ≤ 2.0 mg/dL
* Not pregnant or nursing
* Negative pregnancy test
* Fertile patients must use effective contraception
* Ejection fraction ≥ 45% by MUGA or echocardiogram
* Patients with HIV infection are eligible, provided the following criteria are met:

  * No evidence of co-infection with hepatitis B or C
  * CD4 cell count ≥ 400/mm\^3
  * No evidence of resistant strains of HIV
  * HIV viral load ≤ 10,000 copies HIV RNA/mL (if not on anti-HIV therapy)
  * HIV viral load ≤ 50 copies HIV RNA/mL (if on anti-HIV therapy)
  * No history of AIDS-defining conditions
* No concurrent uncontrolled illness including, but not limited to, the following:

  * Ongoing or active infection
  * Symptomatic congestive heart failure
  * Unstable angina pectoris
  * Cardiac arrhythmia
  * Psychiatric illness/social situation that would limit compliance with study requirements
* No active secondary malignancy except nonmelanomatous skin cancer

PRIOR CONCURRENT THERAPY:

* No prior cytotoxic chemotherapy or rituximab

  * Prior limited course of glucocorticoids allowed
* No other concurrent investigational or commercial anticancer therapies