Here is one way to do it:
def assert_sum_equality(ser1, ser2, ser3, ser4):
"""Helper function.
"""
if ser1.isna().all() and ser2.isna().all():
return True
_ = [ser.fillna(0, inplace=True) for ser in [ser1, ser2, ser3, ser4]]
return all(ser1 + ser2 == ser3 + ser4)
import pandas as pd
# ser1 and ser2 are filled with pd.NA
ser1 = pd.Series({"a": pd.NA, "b": pd.NA, "c": pd.NA, "d": pd.NA, "e": pd.NA})
ser2 = pd.Series({"a": pd.NA, "b": pd.NA, "c": pd.NA, "d": pd.NA, "e": pd.NA})
ser3 = pd.Series({"a": 0, "b": pd.NA, "c": 7, "d": 15, "e": pd.NA})
ser4 = pd.Series({"a": 5, "b": 2, "c": 10, "d": pd.NA, "e": 125})
print(assert_sum_equality(ser1, ser2, ser3, ser4)) # True
# ser1 + ser2 == ser3 + ser4 on all rows
ser1 = pd.Series({"a": 1, "b": 2, "c": 13, "d": 5, "e": 50})
ser2 = pd.Series({"a": 4, "b": pd.NA, "c": 4, "d": 10, "e": 100})
ser3 = pd.Series({"a": 0, "b": pd.NA, "c": 7, "d": 15, "e": pd.NA})
ser4 = pd.Series({"a": 5, "b": 2, "c": 10, "d": pd.NA, "e": 150})
print(assert_sum_equality(ser1, ser2, ser3, ser4)) # True
# ser1 + ser2 != ser3 + ser4 on rows 'c' and 'e'
ser1 = pd.Series({"a": 1, "b": 2, "c": pd.NA, "d": 5, "e": 50})
ser2 = pd.Series({"a": 4, "b": pd.NA, "c": pd.NA, "d": 10, "e": 100})
ser3 = pd.Series({"a": 0, "b": pd.NA, "c": 7, "d": 15, "e": pd.NA})
ser4 = pd.Series({"a": 5, "b": 2, "c": 10, "d": pd.NA, "e": pd.NA})
print(assert_sum_equality(ser1, ser2, ser3, ser4)) # False