Is there a better way to re-use plots Matplotlib?

The below code block (A) solves my overall problem of being able to re-use plots, but i'm wondering if there is a better way (one that doesn't involve creating a function for each plt.plot, as is shown below.

Code block A:

import maptplotlib.pyplot as plt

#create a function just to call the plt.plot
def first_plot(): plt.plot(x,y) 
first_plot()
# Now i can just show the first plot
plt.show()

def second_plot(): plt.plot(x,z)

first_plot() # instead of plt.plot(x,y)
second_plot() # instead of plt.plot(x,z)
# now i can show both plots
plt.show()

if the plots are complicated:

plot.plot(lots of details)

and their are many:

plots = [first,second,third,fourth,...]

I would think this would be advantageous because it avoids code re-use.

However, creating a function just to call plt.plot() indicates to me their might be a better way.what i would like to be doing is something like

first_plot = plt.plot(x,y)
first_plot()
#now i want to show just the first plot
plt.show() # first call

second_plot = plt.plot(x,z)
# now i want to show them together combined
first_plot() 
second_plot()
plt.show() # second call

But this doesn't seem to work/e.g the second call to plt.show() wouldn't produce the first plot. (even if you unpack first_plot (which in reality, from code block B, is actual a list):

In [17]: first_plot
Out[17]: [<matplotlib.lines.Line2D at 0x7fd33ac8ff50>]

This cannot be used to produce the plot again in anyway I can see. This might be because of the relationship between plt.show and plt.plot, which i don't fully understand. Plt.plot seems to put the plot in a que, that then plt.show pops out. However, plt.shows description talks about a blocking and unblocking mode and interactive and non-interactive mode:

show(*args, **kw)
    When running in ipython with its pylab mode, display all
    figures and return to the ipython prompt.

    In non-interactive mode, display all figures and block until
    the figures have been closed; in interactive mode it has no
    effect unless figures were created prior to a change from
    non-interactive to interactive mode (not recommended).  In
    that case it displays the figures but does not block.

    A single experimental keyword argument, *block*, may be
    set to True or False to override the blocking behavior
    described above.

Which i don't understand. But regardless of how i call plt.show() vs plt.show(False) (blocking?) it doesn't seem to have an impact e.g the output is the same in the context of code block A and B.

So put another way, is there a way to select which plots created to show/overlay at different points in the code?