I got the answer of my own question.
We need to use .set_text() command in a loop which updates the text(characteristics of points). Here is the abstract code:
fig1=plt.figure(figsize=(15,32))
ax1=fig1.add_subplot(111, aspect='equal')
ax1.grid(True)
Ln, = ax1.plot(plot_x,plot_y,'ro') #plot_X,plot_y are lists of points
plt.ion() # to make figure interactive
plt.show()
......
......
......
Ln.set_data(plot_x,plot_y) #to updates points in the lists
for i in range(len(plot_ann)): #each time plot_ann number will change
if i >= len(ann_objs): #ann_objs is annotation object list
ann_objs.append(ax1.annotate("", xy=(0,0)))
ann_objs[i].set_text(plot_ann[i])
ann_objs[i].xy = (plot_x[i], plot_y[i])
ann_objs[i].xyann = (plot_x[i]+0.2, plot_y[i]+0.2)