How Service provider will authenticate user has already loggged in IDP?

SAML for ASP.NET
1

I have 3 Service provider applications, and a single IDP, I have successfully authenticated from one of the Service provider.
Now I need to access another two service providers with out login.
How I need to share the SAML Session across different service providers?
Is there any use to store the SAML Response in the browser?

2

The SAML session and SAML responses are not shared.
A SAML response is one-time use only.
Once the first SP has SSO’d to the IdP, and assuming the user still has an authentication session with the IdP, subsequent SSO by the other SPs won’t require the user to login.
For example:
1. SP1 initiates SSO to IdP.
2. There’s no authentication session at the IdP so the user is prompted to login.
3. IdP sends SAML response to SP1.
4. SP2 initiates SSO to IdP.
5. There is an authentication session at the IdP so the user is not prompted to login.
6. IdP sends SAML response to SP2.
7. SP3 initiates SSO to IdP.
8. There is an authentication session at the IdP so the user is not prompted to login.
9. IdP sends SAML response to SP3.