diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 6259a6b3..495104a3 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -8,7 +8,7 @@ jobs:
     runs-on: "ubuntu-latest"
     strategy:
       matrix:
-        python-version: ["3.7", "3.8", "3.9", "3.10", "3.11"]
+        python-version: ["3.7", "3.8", "3.9", "3.10", "3.11", "3.12"]
     steps:
       - uses: actions/checkout@v3
       - name: Set up Python ${{ matrix.python-version }}
diff --git a/datasketch/lsh.py b/datasketch/lsh.py
index 2f1c9b40..4a682f84 100644
--- a/datasketch/lsh.py
+++ b/datasketch/lsh.py
@@ -229,21 +229,21 @@ def insert(
     def merge(
             self,
             other: MinHashLSH,
-            check_disjointness: bool = False      
+            check_overlap: bool = False      
     ):
         """Merge the other MinHashLSH with this one, making this one the union
         of both the MinHashLSH.
 
         Args:
             other (MinHashLSH): The other MinHashLSH.
-            check_duplication (bool): To avoid duplicate keys in the storage
+            check_overlap (bool): Check if there are any overlapping keys before merging and raise if there are any.
                 (`default=True`)
 
         Raises:
             ValueError: If the two MinHashLSH have different initialization
-                parameters.
+                parameters, or if `check_overlap` is `True` and there are overlapping keys.
         """
-        self._merge(other, check_disjointness=check_disjointness, buffer=False)
+        self._merge(other, check_overlap=check_overlap, buffer=False)
 
     def insertion_session(self, buffer_size: int = 50000) -> MinHashLSHInsertionSession:
         """
@@ -304,25 +304,24 @@ def _insert(
     def __equivalent(self, other:MinHashLSH) -> bool:
         """
         Returns:
-            bool: If the two MinHashLSH have equal num_perm, number of bands, size of each band and hashfunc (if provided) then two are equivalent.
+            bool: If the two MinHashLSH have equal num_perm, number of bands, size of each band then two are equivalent.
         """
         return (
             type(self) is type(other) and
             self.h == other.h and
             self.b == other.b and
-            self.r == other.r and
-            type(self.hashfunc) == type(other.hashfunc)
+            self.r == other.r
         )
 
     def _merge(
         self,
         other: MinHashLSH,
-        check_disjointness: bool = False,
+        check_overlap: bool = False,
         buffer: bool = False
     ) -> MinHashLSH:
         if self.__equivalent(other):
-            if check_disjointness and set(self.keys).intersection(set(other.keys)):
-                raise ValueError("The keys are not disjoint, duplicate key exists.")
+            if check_overlap and set(self.keys).intersection(set(other.keys)):
+                raise ValueError("The keys are overlapping, duplicate key exists.")
             for key in other.keys:
                 Hs = other.keys.get(key)
                 self.keys.insert(key, *Hs, buffer=buffer)
diff --git a/examples/lsh_examples.py b/examples/lsh_examples.py
index 6d50563c..007e1399 100644
--- a/examples/lsh_examples.py
+++ b/examples/lsh_examples.py
@@ -47,8 +47,8 @@ def eg1():
 
     lsh1.merge(lsh2)
     print("Does m1 exist in the lsh1...", "m1" in lsh1.keys)
-    # if check_disjointness flag is set to True then it will check the disjointness of the keys in the two MinHashLSH
-    lsh1.merge(lsh2,check_disjointness=True)
+    # if check_overlap flag is set to True then it will check the overlapping of the keys in the two MinHashLSH
+    lsh1.merge(lsh2,check_overlap=True)
 
 def eg2():
     mg = WeightedMinHashGenerator(10, 5)
diff --git a/test/test_lsh.py b/test/test_lsh.py
index c2b080f8..a2893753 100644
--- a/test/test_lsh.py
+++ b/test/test_lsh.py
@@ -273,14 +273,24 @@ def test_merge(self):
             self.assertTrue("c" in lsh1.hashtables[i][H])
 
         self.assertTrue(lsh1.merge, lsh2)
-        self.assertRaises(ValueError, lsh1.merge, lsh2, check_disjointness=True)
+        self.assertRaises(ValueError, lsh1.merge, lsh2, check_overlap=True)
 
-        m5 = MinHash(32)
+        m5 = MinHash(16)
         m5.update("e".encode("utf-8"))
-        lsh3 = MinHashLSH(threshold=0.5, num_perm=32)
+        lsh3 = MinHashLSH(threshold=0.5, num_perm=16)
         lsh3.insert("a",m5)
 
-        self.assertRaises(ValueError, lsh1.merge, lsh3, check_disjointness=True)
+        self.assertRaises(ValueError, lsh1.merge, lsh3, check_overlap=True)
+
+        lsh1.merge(lsh3)
+
+        m6 = MinHash(16)
+        m6.update("e".encode("utf-8"))
+        lsh4 = MinHashLSH(threshold=0.5, num_perm=16)
+        lsh4.insert("a",m6)
+
+        lsh1.merge(lsh4, check_overlap=False)
+
 
     def test_merge_redis(self):
         with patch('redis.Redis', fake_redis) as mock_redis:
@@ -321,16 +331,26 @@ def test_merge_redis(self):
                 self.assertTrue(pickle.dumps("c") in lsh1.hashtables[i][H])
 
             self.assertTrue(lsh1.merge, lsh2)
-            self.assertRaises(ValueError, lsh1.merge, lsh2, check_disjointness=True)
+            self.assertRaises(ValueError, lsh1.merge, lsh2, check_overlap=True)
 
-            m5 = MinHash(32)
+            m5 = MinHash(16)
             m5.update("e".encode("utf-8"))
-            lsh3 = MinHashLSH(threshold=0.5, num_perm=32, storage_config={
+            lsh3 = MinHashLSH(threshold=0.5, num_perm=16, storage_config={
                 'type': 'redis', 'redis': {'host': 'localhost', 'port': 6379}
             })
             lsh3.insert("a",m5)
 
-            self.assertRaises(ValueError, lsh1.merge, lsh3, check_disjointness=True)
+            self.assertRaises(ValueError, lsh1.merge, lsh3, check_overlap=True)
+
+            m6 = MinHash(16)
+            m6.update("e".encode("utf-8"))
+            lsh4 = MinHashLSH(threshold=0.5, num_perm=16, storage_config={
+                'type': 'redis', 'redis': {'host': 'localhost', 'port': 6379}
+            })
+            lsh4.insert("a",m6)
+            
+            lsh1.merge(lsh4, check_overlap=False)
+
 
 class TestWeightedMinHashLSH(unittest.TestCase):