Nervous bank customers have rushed to the safety of big banks in the wake of a pair of high-profile bank failures that have shaken confidence in the system. Bank of America\n \n (BAC), Wells Fargo\n \n (WFC) and Citigroup\n \n (C) have all experienced a significant increase in deposits since Silicon Valley Bank ran into trouble last week, people familiar with the matter tell CNN. Small and regional banks have suffered deposit outflows, though a senior Treasury official told CNN earlier this week that those customer withdrawals have eased. The situation is fluid and it’s not clear just how much money has been plowed into big banks, though the sum is likely to be in the billions or tens of billions of dollars. Last Thursday alone customers yanked $42 billion from Silicon Valley Bank, draining the California lender of all of its cash. By Friday, regulators shut the bank down, making it the second largest bank failure in American history. In the past week, Citi has been speeding up account openings across retail banking, small business lending and wealth management, a person familiar with the matter said. Bank of America has raked in more than $15 billion in new deposits in the span of just days, Bloomberg News reports. Banks don’t typically disclose specifics on short-term swings in deposits, opting to release these figures on a quarterly basis. Bank of America, Wells Fargo and Citi declined to comment. Big banks are perceived to be safer because of their larger balance sheets. Moreover, their role as systemically important institutions suggests the government would come to their rescue in the event of trouble, as they did in 2008. But the FDIC insures deposits up to $250,000 per bank per borrower, regardless of if the accounts are at small, medium or large banks. Analysts say the FDIC’s decision to rescue uninsured depositors at Silicon Valley Bank and Signature Bank suggests regulators would be forced to do the same if another bank collapsed.