The builtin threading.Thread class offers all you need: start to start a new thread and join to wait for the end of a thread.
import threading
def task1():
pass
def task2():
pass
def task3():
pass
def task4():
pass
def task5():
pass
def task6():
pass
def dep1():
t1 = threading.Thread(target=task1)
t2 = threading.Thread(target=task2)
t3 = threading.Thread(target=task3)
t1.start()
t2.start()
t3.start()
t1.join()
t2.join()
t3.join()
def dep2():
t4 = threading.Thread(target=task4)
t5 = threading.Thread(target=task5)
t4.start()
t5.start()
t4.join()
t5.join()
def dep3():
d1 = threading.Thread(target=dep1)
d2 = threading.Thread(target=dep2)
d1.start()
d2.start()
d1.join()
d2.join()
d3 = threading.Thread(target=dep3)
d3.start()
d3.join()
Alternatively to join you can use Queue.join to wait for the threads end.