Three pharmacy benefit managers (PBMs) - CVS's Caremark, Cigna's Express Scripts and UnitedHealth Group's Optum Rx - currently control around 80% of the U.S. prescription drug market.

Tyson has become one of the largest U.S. employers to move away from using a traditional PBM, at a time when these companies are under fire from lawmakers over their role in driving up healthcare costs.

Last year, non-profit health insurer Blue Shield of California said it plans to stop using most of CVS's PBM services and tap into five different partners, including Amazon.com and Mark Cuban's Cost Plus Drugs.

Rightway works on a fee basis and claims it can reduce employer spending by 18% on average. The startup also said it allows clients to trace every transaction to boost transparency.

PBMs act as middlemen, negotiating rebates and fees with drug manufacturers, creating lists of medications that are covered by insurance and reimbursing pharmacies for patients' prescriptions.

In December, CVS had said it would simplify the structure through which its pharmacies get reimbursed for drugs, in a push for more transparency.

Under the new model, called CostVantage, the company's over-9,000 pharmacies will have fixed markups and fees to define drug costs and related reimbursements at contracted insurers and pharmacy benefit managers.

Tyson and CVS did not immediately respond to Reuters requests for comment.

(Reporting by Christy Santhosh and Granth Vanaik; Editing by Anil D'Silva, Shweta Agarwal and Pooja Desai)