diff --git a/pandas/core/reshape/merge.py b/pandas/core/reshape/merge.py
index c01bf3931b27a..5ceac80c340ba 100644
--- a/pandas/core/reshape/merge.py
+++ b/pandas/core/reshape/merge.py
@@ -10,6 +10,8 @@
 import string
 from typing import (
     TYPE_CHECKING,
+    Hashable,
+    List,
     Optional,
     Tuple,
     cast,
@@ -124,14 +126,13 @@ def merge(
     merge.__doc__ = _merge_doc % "\nleft : DataFrame"
 
 
-def _groupby_and_merge(by, on, left: DataFrame, right: DataFrame, merge_pieces):
+def _groupby_and_merge(by, left: DataFrame, right: DataFrame, merge_pieces):
     """
     groupby & merge; we are always performing a left-by type operation
 
     Parameters
     ----------
     by: field to group
-    on: duplicates field
     left: DataFrame
     right: DataFrame
     merge_pieces: function for merging
@@ -307,9 +308,7 @@ def _merger(x, y):
         check = set(left_by).difference(left.columns)
         if len(check) != 0:
             raise KeyError(f"{check} not found in left columns")
-        result, _ = _groupby_and_merge(
-            left_by, on, left, right, lambda x, y: _merger(x, y)
-        )
+        result, _ = _groupby_and_merge(left_by, left, right, lambda x, y: _merger(x, y))
     elif right_by is not None:
         if isinstance(right_by, str):
             right_by = [right_by]
@@ -317,7 +316,7 @@ def _merger(x, y):
         if len(check) != 0:
             raise KeyError(f"{check} not found in right columns")
         result, _ = _groupby_and_merge(
-            right_by, on, right, left, lambda x, y: _merger(y, x)
+            right_by, right, left, lambda x, y: _merger(y, x)
         )
     else:
         result = _merger(left, right)
@@ -708,7 +707,7 @@ def __init__(
         if validate is not None:
             self._validate(validate)
 
-    def get_result(self):
+    def get_result(self) -> DataFrame:
         if self.indicator:
             self.left, self.right = self._indicator_pre_merge(self.left, self.right)
 
@@ -774,7 +773,7 @@ def _indicator_pre_merge(
 
         return left, right
 
-    def _indicator_post_merge(self, result):
+    def _indicator_post_merge(self, result: DataFrame) -> DataFrame:
 
         result["_left_indicator"] = result["_left_indicator"].fillna(0)
         result["_right_indicator"] = result["_right_indicator"].fillna(0)
@@ -790,7 +789,7 @@ def _indicator_post_merge(self, result):
         result = result.drop(labels=["_left_indicator", "_right_indicator"], axis=1)
         return result
 
-    def _maybe_restore_index_levels(self, result):
+    def _maybe_restore_index_levels(self, result: DataFrame) -> None:
         """
         Restore index levels specified as `on` parameters
 
@@ -949,7 +948,6 @@ def _get_join_info(self):
                         self.left.index,
                         self.right.index,
                         left_indexer,
-                        right_indexer,
                         how="right",
                     )
                 else:
@@ -961,7 +959,6 @@ def _get_join_info(self):
                         self.right.index,
                         self.left.index,
                         right_indexer,
-                        left_indexer,
                         how="left",
                     )
                 else:
@@ -979,9 +976,8 @@ def _create_join_index(
         index: Index,
         other_index: Index,
         indexer,
-        other_indexer,
         how: str = "left",
-    ):
+    ) -> Index:
         """
         Create a join index by rearranging one index to match another
 
@@ -1126,7 +1122,7 @@ def _get_merge_keys(self):
 
         return left_keys, right_keys, join_names
 
-    def _maybe_coerce_merge_keys(self):
+    def _maybe_coerce_merge_keys(self) -> None:
         # we have valid merges but we may have to further
         # coerce these if they are originally incompatible types
         #
@@ -1285,7 +1281,7 @@ def _create_cross_configuration(
             cross_col,
         )
 
-    def _validate_specification(self):
+    def _validate_specification(self) -> None:
         if self.how == "cross":
             if (
                 self.left_index
@@ -1372,7 +1368,7 @@ def _validate_specification(self):
         if self.how != "cross" and len(self.right_on) != len(self.left_on):
             raise ValueError("len(right_on) must equal len(left_on)")
 
-    def _validate(self, validate: str):
+    def _validate(self, validate: str) -> None:
 
         # Check uniqueness of each
         if self.left_index:
@@ -1479,10 +1475,10 @@ def restore_dropped_levels_multijoin(
     left: MultiIndex,
     right: MultiIndex,
     dropped_level_names,
-    join_index,
-    lindexer,
-    rindexer,
-):
+    join_index: Index,
+    lindexer: np.ndarray,
+    rindexer: np.ndarray,
+) -> Tuple[List[Index], np.ndarray, List[Hashable]]:
     """
     *this is an internal non-public method*
 
@@ -1500,7 +1496,7 @@ def restore_dropped_levels_multijoin(
         right index
     dropped_level_names : str array
         list of non-common level names
-    join_index : MultiIndex
+    join_index : Index
         the index of the join between the
         common levels of left and right
     lindexer : intp array
@@ -1514,8 +1510,8 @@ def restore_dropped_levels_multijoin(
         levels of combined multiindexes
     labels : intp array
         labels of combined multiindexes
-    names : str array
-        names of combined multiindexes
+    names : List[Hashable]
+        names of combined multiindex levels
 
     """
 
@@ -1604,7 +1600,7 @@ def __init__(
             sort=True,  # factorize sorts
         )
 
-    def get_result(self):
+    def get_result(self) -> DataFrame:
         join_index, left_indexer, right_indexer = self._get_join_info()
 
         llabels, rlabels = _items_overlap_with_suffix(
@@ -1653,7 +1649,7 @@ def _asof_by_function(direction: str):
 }
 
 
-def _get_cython_type_upcast(dtype):
+def _get_cython_type_upcast(dtype) -> str:
     """ Upcast a dtype to 'int64_t', 'double', or 'object' """
     if is_integer_dtype(dtype):
         return "int64_t"