As I noted in my other thread, you use a coupling capacitor between stages with a pull-up resistor to the V+ at the output of the capacitor (the trigger input to the next stage). See the circuit on the right at **broken link removed** for example, where the preceding 555 output substitutes for the push-button. You just need the time-constant of the RC to be less then the 555 period of the stage being driven. A 10kΩ pull-up with a 0.1µF coupling cap will have a time-constant of 1ms, which is well below your minimum time of 1s. Add a diode across the pull-up resistor (cathode to V+) as shown in the referenced circuit to shunt the positive portion of the pulse when the driving 555 output goes high at the start of its period.