diff --git a/pandas/_libs/index.pyx b/pandas/_libs/index.pyx
index f1f56c6c0c855..f7cec262ca302 100644
--- a/pandas/_libs/index.pyx
+++ b/pandas/_libs/index.pyx
@@ -74,6 +74,7 @@ cdef class IndexEngine:
         return val in self.mapping
 
     cpdef get_loc(self, object val):
+        # -> Py_ssize_t | slice | ndarray[bool]
         cdef:
             Py_ssize_t loc
 
@@ -109,6 +110,7 @@ cdef class IndexEngine:
             raise KeyError(val)
 
     cdef inline _get_loc_duplicates(self, object val):
+        # -> Py_ssize_t | slice | ndarray[bool]
         cdef:
             Py_ssize_t diff
 
@@ -142,6 +144,7 @@ cdef class IndexEngine:
     cdef _unpack_bool_indexer(self,
                               ndarray[uint8_t, ndim=1, cast=True] indexer,
                               object val):
+        # Returns ndarray[bool] or int
         cdef:
             ndarray[intp_t, ndim=1] found
             int count
diff --git a/pandas/_libs/index_class_helper.pxi.in b/pandas/_libs/index_class_helper.pxi.in
index 8638c2c689c3f..f0351e06f2b8c 100644
--- a/pandas/_libs/index_class_helper.pxi.in
+++ b/pandas/_libs/index_class_helper.pxi.in
@@ -44,8 +44,8 @@ cdef class {{name}}Engine(IndexEngine):
             raise KeyError(val)
     {{endif}}
 
-    cdef void _call_map_locations(self, ndarray values):
-        self.mapping.map_locations(algos.ensure_{{name.lower()}}(values))
+    cdef void _call_map_locations(self, ndarray[{{dtype}}_t] values):
+        self.mapping.map_locations(values)
 
     cdef _maybe_get_bool_indexer(self, object val):
         # Returns ndarray[bool] or int
diff --git a/pandas/_libs/intervaltree.pxi.in b/pandas/_libs/intervaltree.pxi.in
index 1af5b23e3393f..0fb01a2188a57 100644
--- a/pandas/_libs/intervaltree.pxi.in
+++ b/pandas/_libs/intervaltree.pxi.in
@@ -73,7 +73,7 @@ cdef class IntervalTree(IntervalMixin):
         self.root = node_cls(self.left, self.right, indices, leaf_size)
 
     @property
-    def left_sorter(self):
+    def left_sorter(self) -> np.ndarray:
         """How to sort the left labels; this is used for binary search
         """
         if self._left_sorter is None:
@@ -81,7 +81,7 @@ cdef class IntervalTree(IntervalMixin):
         return self._left_sorter
 
     @property
-    def right_sorter(self):
+    def right_sorter(self) -> np.ndarray:
         """How to sort the right labels
         """
         if self._right_sorter is None:
@@ -89,7 +89,7 @@ cdef class IntervalTree(IntervalMixin):
         return self._right_sorter
 
     @property
-    def is_overlapping(self):
+    def is_overlapping(self) -> bool:
         """
         Determine if the IntervalTree contains overlapping intervals.
         Cached as self._is_overlapping.
@@ -109,7 +109,7 @@ cdef class IntervalTree(IntervalMixin):
         return self._is_overlapping
 
     @property
-    def is_monotonic_increasing(self):
+    def is_monotonic_increasing(self) -> bool:
         """
         Return True if the IntervalTree is monotonic increasing (only equal or
         increasing values), else False
@@ -119,7 +119,7 @@ cdef class IntervalTree(IntervalMixin):
         sort_order = np.lexsort(values)
         return is_monotonic(sort_order, False)[0]
 
-    def get_indexer(self, scalar_t[:] target):
+    def get_indexer(self, scalar_t[:] target) -> np.ndarray:
         """Return the positions corresponding to unique intervals that overlap
         with the given array of scalar targets.
         """
@@ -180,7 +180,7 @@ cdef class IntervalTree(IntervalMixin):
                     n_elements=self.root.n_elements))
 
     # compat with IndexEngine interface
-    def clear_mapping(self):
+    def clear_mapping(self) -> None:
         pass
 
 
diff --git a/pandas/_libs/sparse.pyx b/pandas/_libs/sparse.pyx
index 0c3d8915b749b..134883e159407 100644
--- a/pandas/_libs/sparse.pyx
+++ b/pandas/_libs/sparse.pyx
@@ -618,6 +618,7 @@ cdef class BlockIndex(SparseIndex):
         pass
 
 
+@cython.internal
 cdef class BlockMerge:
     """
     Object-oriented approach makes sharing state between recursive functions a
@@ -661,6 +662,7 @@ cdef class BlockMerge:
             self.yi = xi
 
 
+@cython.internal
 cdef class BlockUnion(BlockMerge):
     """
     Object-oriented approach makes sharing state between recursive functions a
diff --git a/pandas/_libs/tslibs/conversion.pxd b/pandas/_libs/tslibs/conversion.pxd
index 1b99e855da40f..5b80193c1f27a 100644
--- a/pandas/_libs/tslibs/conversion.pxd
+++ b/pandas/_libs/tslibs/conversion.pxd
@@ -28,7 +28,7 @@ cdef _TSObject convert_datetime_to_tsobject(datetime ts, tzinfo tz,
 
 cdef int64_t get_datetime64_nanos(object val) except? -1
 
-cpdef datetime localize_pydatetime(datetime dt, object tz)
+cpdef datetime localize_pydatetime(datetime dt, tzinfo tz)
 cdef int64_t cast_from_unit(object ts, str unit) except? -1
 cpdef (int64_t, int) precision_from_unit(str unit)
 
diff --git a/pandas/_libs/tslibs/conversion.pyx b/pandas/_libs/tslibs/conversion.pyx
index 1bda35206ccef..865185f9acea7 100644
--- a/pandas/_libs/tslibs/conversion.pyx
+++ b/pandas/_libs/tslibs/conversion.pyx
@@ -810,14 +810,14 @@ cdef inline datetime _localize_pydatetime(datetime dt, tzinfo tz):
         return dt.replace(tzinfo=tz)
 
 
-cpdef inline datetime localize_pydatetime(datetime dt, object tz):
+cpdef inline datetime localize_pydatetime(datetime dt, tzinfo tz):
     """
     Take a datetime/Timestamp in UTC and localizes to timezone tz.
 
     Parameters
     ----------
     dt : datetime or Timestamp
-    tz : tzinfo, "UTC", or None
+    tz : tzinfo or None
 
     Returns
     -------