Consider the following question: If two nodes collide what do you get? 
First of all it can not be a strict $A\_2$ node, because the delta invariant 
of that is $1$. So it has to be more singular than an $A\_2$ node. It can 
be an $A\_3$ node because the delta invariant of that is $2$. 


Is there any simple argument to show that if an $A\_2$ node and an $A\_1$ node 
collide, then we can not get a strict $A\_3$ node? The delta invariant doesn't 
help. Is there some other invariant that can answer this question?
Note that I am NOT asking what do we actually get when an $A\_2$ node and 
an $A\_1$ node collide. I merely want to show that we can not get a 
strict $A\_3$ node. 



Is there an invariant similar to the delta invariant that distinguishes an $A_2$ node form an $A_1$ node? 
I am not sure if the following counts as a simple argument: 


A miniversal deformation of the $A\_3$ singularity is given by the family $y^2 = a + bx + cx^2 + x^4$. There is no member in this family with nodes of type $A\_1$ and $A\_2$ so it follows that we cannot get an $A\_3$ node from collisions of two nodes of type $A\_1$ and $A\_2$.


