How can a method of base class access the global variable declared in another method of the base class that has been overwritten?

Assume there are two files of Python, the first file defines a class:

File1: test1.py

class C1(object):
   def __init__(self):
       pass

   def method1(self):
      global v1
      v1 = "cat"
      self.method2()
    
   def method2(self):
      print(v1)

The second file define another class, which is derived from the first class from the first file:

File2: test2.py

from test1 import C1

class C2(C1):
   def __init__(self):
       super(C2, self).__init__()

   def method1(self):
       global v1
       v1 = "dog"
       self.method2()

The following is the test code:

c2 = C2()
c2.method1()

An error will occur:

NameError: name 'v1' is not defined

I want to overwrite the method 'method1' only, how can the global variable 'v1' in C2 be accessed by the method2 in C1?