jupyter notebook matplotlib show plot and then plot on the origin figure - matplotlib

Question

I want to plot a white plot with two axes, show it to the user, then add a line to the white plot with two axes, show it to the user, then add some dot to the line, then show it to the user. How can I do this without copying the code again and again?
What I'm doing now is in the first code chunk
import math
import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline
fig = plt.figure(figsize=(5,5))
ax = plt.axes()
ax.set_xlabel('cat')
ax.set_ylabel('dog')
plt.title("Set of 2 animals")
plt.show()
then in the second code chunk
fig = plt.figure(figsize=(5,5))
ax = plt.axes()
x = np.linspace(0, 1.0, 1000)
ax.plot(x, 1.0-x,zorder = 0)
ax.set_xlabel('cat')
ax.set_ylabel('dog')
plt.title("Set of 2 animals")
plt.show()
then in the third code chunk
fig = plt.figure(figsize=(5,5))
ax = plt.axes()
x = np.linspace(0, 1.0, 1000)
ax.plot(x, 1.0-x,zorder = 0)
ax.set_xlabel('cat')
ax.set_ylabel('dog')
plt.title("Set of 2 animals")
p0 = 0.5
p1 = 0.5
color = "blue"
textd =0.05
ax.scatter([p0],[p1], color = color,zorder=1)
ax.text(p0+textd, p1+textd, 'tiger',color = color,zorder =2)
plt.show()
What I'm looking for is things like in the first code chunk
import math
import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline
fig = plt.figure(figsize=(5,5))
ax = plt.axes()
ax.set_xlabel('cat')
ax.set_ylabel('dog')
plt.title("Set of 2 animals")
plt.show()
then in the second code chunk
add line directly without duplicating the code for making axes
plt.show()
then in the third code chunk
add point directly without duplicating the code for making axes and lines
plt.show()

Answer 1

Update: I actually figured out the answer.
def plot(step):
fig = plt.figure(figsize=(5,5))
ax = plt.axes()
ax.set_xlabel('cat')
ax.set_ylabel('dog')
plt.title("Set of 2 animals")
if step>=1:
x = np.linspace(0, 1.0, 1000)
ax.plot(x, 1.0-x,zorder = 0)
if step>=2:
p0 = 0.5
p1 = 0.5
color = "blue"
textd =0.05
ax.scatter([p0],[p1], color = color,zorder=1)
ax.text(p0+textd, p1+textd, 'tiger',color = color,zorder =2)
plot.show()
should be able to solve the problem.