efficent emergency connection

the purpose of such a connection is, I want to connect 2 mobile battery , long time power supply for output 3 leds. I want to use 1 battery at atime when another is off automatically (reverse bias turn the attery off). after some time when battery_1 is discharging and supply voltage get decreases then battery_2 turn on automatically and battery_1 turn off automatically. thus we can use 2 battery for a long time power supply.