"About 1420 Alice, Countess of Salisbury, married Sir Richard Neville, who became Earl of Warwick".
He was never Earl of Warwick. He was a younger son, by a second marriage, of Ralph Earl of Westmorland and so not heir to the (Westmorland) earldom. He became jure uxoris (by right of his wife) Earl of Salisbury by his marriage to Alice, daughter and heiress of Thomas Montacute 4th Earl of Salisbury.
His son Richard was betrothed at six years old to Anne Beauchamp, daughter of Richard de Beauchamp 13th Earl of Warwick and his wife Isabel Despenser. Thus he became heir to a substantial part of the Montague, Beauchamp, and Despenser inheritance as well as the earldom of Salisbury.
When Beauchamp's son Henry, who was married to Richard's sister Cecily, died in 1446 followed by Henry's daughter Anne in 1449, Richard found himself jure uxonis Earl of Warwick. There then followed a protracted battle over parts of the inheritance, particularly with Edmund Beaufort, 1st Duke of Somerset, who was married to a daughter from Richard Beauchamp's first marriage. The dispute was about land, not about the Warwick title, as Henry's half-sisters were excluded from the succession.