diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 444150748208..1b0445a039a7 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -1,5 +1,6 @@
 from collections import OrderedDict
 from contextlib import ExitStack
+import functools
 import inspect
 import itertools
 import logging
@@ -562,13 +563,10 @@ def __init__(self, fig, rect,
 
         self.update(kwargs)
 
-        if self.xaxis is not None:
-            self._xcid = self.xaxis.callbacks.connect(
-                'units finalize', lambda: self._on_units_changed(scalex=True))
-
-        if self.yaxis is not None:
-            self._ycid = self.yaxis.callbacks.connect(
-                'units finalize', lambda: self._on_units_changed(scaley=True))
+        for name, axis in self._get_axis_map().items():
+            axis.callbacks._pickled_cids.add(
+                axis.callbacks.connect(
+                    'units finalize', self._unit_change_handler(name)))
 
         rcParams = mpl.rcParams
         self.tick_params(
@@ -2150,14 +2148,17 @@ def add_container(self, container):
         container._remove_method = self.containers.remove
         return container
 
-    def _on_units_changed(self, scalex=False, scaley=False):
+    def _unit_change_handler(self, axis_name, event=None):
         """
-        Callback for processing changes to axis units.
-
-        Currently requests updates of data limits and view limits.
+        Process axis units changes: requests updates to data and view limits.
         """
+        if event is None:  # Allow connecting `self._unit_change_handler(name)`
+            return functools.partial(
+                self._unit_change_handler, axis_name, event=object())
+        _api.check_in_list(self._get_axis_map(), axis_name=axis_name)
         self.relim()
-        self._request_autoscale_view(scalex=scalex, scaley=scaley)
+        self._request_autoscale_view(scalex=(axis_name == "x"),
+                                     scaley=(axis_name == "y"))
 
     def relim(self, visible_only=False):
         """
diff --git a/lib/matplotlib/lines.py b/lib/matplotlib/lines.py
index 479ae162112b..af92fadf79d9 100644
--- a/lib/matplotlib/lines.py
+++ b/lib/matplotlib/lines.py
@@ -627,13 +627,9 @@ def axes(self, ax):
         # call the set method from the base-class property
         Artist.axes.fset(self, ax)
         if ax is not None:
-            # connect unit-related callbacks
-            if ax.xaxis is not None:
-                self._xcid = ax.xaxis.callbacks.connect('units',
-                                                        self.recache_always)
-            if ax.yaxis is not None:
-                self._ycid = ax.yaxis.callbacks.connect('units',
-                                                        self.recache_always)
+            for axis in ax._get_axis_map().values():
+                axis.callbacks._pickled_cids.add(
+                    axis.callbacks.connect('units', self.recache_always))
 
     def set_data(self, *args):
         """
diff --git a/lib/mpl_toolkits/mplot3d/axes3d.py b/lib/mpl_toolkits/mplot3d/axes3d.py
index 106a12b9f2bf..605bf8325291 100644
--- a/lib/mpl_toolkits/mplot3d/axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/axes3d.py
@@ -11,6 +11,7 @@
 """
 
 from collections import defaultdict
+import functools
 from functools import reduce
 from itertools import compress
 import math
@@ -111,12 +112,6 @@ def __init__(
         # func used to format z -- fall back on major formatters
         self.fmt_zdata = None
 
-        if self.zaxis is not None:
-            self._zcid = self.zaxis.callbacks.connect(
-                'units finalize', lambda: self._on_units_changed(scalez=True))
-        else:
-            self._zcid = None
-
         self.mouse_init()
         self.figure.canvas.callbacks._pickled_cids.update({
             self.figure.canvas.mpl_connect(
@@ -475,14 +470,16 @@ def get_axis_position(self):
         zhigh = tc[0][2] > tc[2][2]
         return xhigh, yhigh, zhigh
 
-    def _on_units_changed(self, scalex=False, scaley=False, scalez=False):
-        """
-        Callback for processing changes to axis units.
-
-        Currently forces updates of data limits and view limits.
-        """
+    def _unit_change_handler(self, axis_name, event=None):
+        # docstring inherited
+        if event is None:  # Allow connecting `self._unit_change_handler(name)`
+            return functools.partial(
+                self._unit_change_handler, axis_name, event=object())
+        _api.check_in_list(self._get_axis_map(), axis_name=axis_name)
         self.relim()
-        self.autoscale_view(scalex=scalex, scaley=scaley, scalez=scalez)
+        self.autoscale_view(scalex=(axis_name == "x"),
+                            scaley=(axis_name == "y"),
+                            scalez=(axis_name == "z"))
 
     def update_datalim(self, xys, **kwargs):
         pass