I see, thanks, although you are saying that the HIGH/LOW Open/Closed status relationship depends on the relay board?
The relays may need to be driven HIGH or LOW in order to be energised. Which it is depends on the design of the relay board. It is common for them to be energised when their input is LOW.
The suggested way to initialise such relays is to set their inputs to HIGH before setting the pinMode() thus ensuring that they are not briefly energised when the pinMode() is applied.
Of course, all of this depends on how the relay inputs are wired and how their outputs are wired. If the relays have changeover outputs then you may decide to have the relays start energised and deal with the outputs appropriately. That, however, will mean that when the Arduino is turned off the normally closed relay contacts will pass current. Whether this is desirable depends on the application.